Important Mechanical Properties Of Solids Questions for CBSE Class 11th

Identify the correct answer. When a very long rod suspended in air will break under its own weight. The maximum length of the rod will depend on a) Breaking stress b) Density c) Cross-sectional area d) Acceleration due to gravity

Pressure of a medium is changed from 1 . 01 x 10 5 N / m 2 to 1 . 11 x 10 5 N / m 2 and change in volume is 5% keeping temperature constant. The bulk modulus of the medium is,

When a 4 kg mass is hung vertically on a light spring that obeys Hooke’s law, the spring stretches by 2 cm. The work required to be done by an external agent in stretching this spring by 5 cm will be (g =10 m/sec 2 )

The breaking stress for a metal is 7.8 × 10 9 Nm − 2 . The density of the metal is 7800 kgm − 3 . If g = 10 N kg − 1 , Find the maximum length of the wire (in km) made of this metal which may be suspended without breaking.

A stress of 10 6 Nm − 2 is required for breaking a material. If the density of the material is 3 × 10 3 kgm − 3 , then what should be the length of the wire made of this material, so that it breaks under its own weight?

A wire of length 2 m is made from 10 cm 3 of copper. A force F is applied so that its length increases by 2 mm. Another wire of length 8 m is made from the same volume of copper. If the force F is applied to it, its length will increase by

A body of mass m = 10 k g is attached to one end of a wire of length 0.3 m. The maximum angular speed (in rad s − 1 ) with which it can be rotated about its other end in space station is (Breaking stress of wire = 4.8 × 10 7 N m − 2 and area of cross section of the wire = 10 − 2 c m 2 ) is :

A uniform rectangular block of mass 50 kg is hung horizontally with the help of three wirres A, B and C each of length and area of 2 m and 10 mm 2 respectively as shown in the figure. The central wire is passing through the centre of gravity and is made of a material of Young's modulus 7.5 × 10 10 Nm –2 and the other two wires A and C symmetrically placed on either side of the wire B are of Young's modulus 10 11 Nm –2 . The tension in the wires A and B will be in the ratio of

A 5 m aluminium wire ( Y= 7 x 10 10 N/m 2 ) of diameter 3 mm supports a 40 kg mass. In order to have the same elongation in a copper wire (Y = 12 x 10 10 N/m 2 ) of the same length under the same weight, the diameter should be (in mm):

The adjacent graph shows the extension ( ∆ I ) of a wire of length 1m suspended from the top of a roof at one end with a load W connected to the other end. If the cross sectional area of the wire is 10 – 6 m 2 , calculate the young’s modulus of the material of the wire

For a constant hydraulic stress on an object, the fractional change in the object’s volume ( ∆ V V ) and its bulk modulus (b) are related as

A uniform cylindrical wire is subjected to a longitudinal tensile stress of 5 × 10 7 Nm – 2 . The Young’s modulus of the material of the wire is 2 × 10 11 Nm – 2 . The volume change in the wire is 0.02%. The factional change in the radius is

A wire of length L and radius r is rigidly fixed at one end. On stretching the other end of the wire with a force F, the increase in its length is l. If another wire of same material but of length 2L and radius 2r is stretched with a force of 2F, the increase in its length will be

The length of an elastic string is a metre when the longitudinal tension is 4 N and b metre when the longitudinal tension is 5 N. The length of the string in metre when the longitudinal tension is 9 N is

In the figure shown, forces of equal magnitude are applied to the two ends of a uniform rod. Consider A as the cross sectional area of the rod. For this situation, mark out the incorrect statements.

Two wires of the same length and same material but radii in the ratio of 1:2 are stretched by unequal forces to produce equal elongation. The ratio of the two forces is

cube is shifted to a depth of 100 m in a lake. The change in volume is 0. 1%. The bulk modulus of the material is nearly

A material has normal density ρ and bulk modulus K. The increase in the density of the material when it is subjected to an external pressure P from all sides is

A metal cube of side 10 cm is subjected to a shearing stress of 10 6 N / m 2 . Calculate the modulus of rigidity in × 10 8 Nm − 2 if the top of the cube is displaced by 0.05 cm with respect to its bottom.

An area of cross-section of rubber string is 2 cm 2 . Its length is doubled when stretched with a linear force of 2 × 10 5 dynes. The Young’s modulus of the rubber in dyne / cm 2 will be

Why the spring is made up of steel in comparison of copper

A weight of 200 kg is suspended by vertical wire of length 600.5 cm. The area of cross-section of wire is 1 mm 2 . When the load is removed, the wire contracts by 0.5 cm. The Young’s modulus of the material of wire will be

An aluminum rod (Young’s modulus = 7 × 10 9 N / m 2 ) has a breaking strain of 0.2%. The minimum cross-sectional area of the rod in order to support a load of 10 4 Newton’s is

A fixed volume of iron is drawn into a wire of length L. The extension produced in this wire by constant force F is proportional to

The stress-strain graph of an elastomer such as tissue of aorta is as shown in the diagram. From the graph which of the following can we infer? As stress increases

The youngs modulus of the material of a rod is 20 ×10 10 pascal. When the longitudinal strain is 0.04%, The energy stored per unit volume is

The graph shows the change x in the length of a wire by the application of a force F at two different temperatures T 1 and T 2 respectively. Then

When an elastic material with Young’s modulus Y is subjected to stretching stress S the elastic energy stored per unit volume of the material is:

The load versus elongation graph for four wires of the same material is shown in the Fig. The thinnest wire is represented by the line:

A uniform metal rod of 2 mm 2 cross-section is heated from 0 °C to 20°C. The coefficient of linear expansion of the rod is 12 x 10 -6 / °C. Its Young’s modulus of elasticity is 10 11 N /m 2 . The energy stored per unit volume of the rod is:

Two wires are made of the same material and have the same volume. The first’ wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by X on applying a force F, how much force is needed to stretch the second wire by the same amount?

For a given material, the value of f is 2.4 times that of η . Its Poisson’s ratio is:

Fig. shows a wire of length l and of slightly non-uniform cross-section. Its radius at one end is R 1 and at the other, it is R 2 The wire is stretched by forces F and F applied along the length in opposite directions and normal to the ends. Y being the Young’s rpodulus, extension caused in the wire is nearly: .

Consider the following statements. (A) Young’s modulus for a perfectly plastic body is zero. (B) For a perfectly plastic body, restoring force is zero Select the correct option. (a)(A) is false, But (B) is true. (b) Both (A) and (B)are true. (c) (A) is true, But (B) is false. (d) Both (A)and(B)are false.

A copper wire ( Y = 10 11 Nm – 2 ) of length 8 m and steel wire ( Y = 2 × 10 11 Nm – 2 ) of length 4 m and each of cross-sectional area 0.5 cm 2 are fastened end to end and stretched with a tension of 500 N. Match the given columns and select the correct option from the codes given below. Column-I Column-II i. elongation in copper wire(in mm) p. 0.2 ii. elongation in steel wire(in mm) q. 1.0 iii. total elongation (in mm) r. 0.8 s. 0.1 t. 0.9 Codes

The average depth of Indian Ocean is about 3000 m. The fractional compression, ∆ V V of water at the bottom of the ocean is (Given : Bulk modulus of the water = 2.2 x 10 9 N m – 2 and g =10 ms – 2 )

The stress-strain graph for a metal wire is as shown in the figure. In the graph, the region in which Hooke’s law is obeyed, the ultimate strength and fracture points are represented by

If two equal and opposite deforming forces are applied parallel to the cross-sectional area of the cylinder as shown in the figure, there is a relative displacement between the opposite faces of the cylinder. The ratio of Δx to L is known as

Density of a material is 8000 Kg/m 3 and permissible stress of this material is 2000 N/cm 2 . Then maximum length of a rod made of this material, that can be kept vertically on the surface of the rod is

One end of a 1 m long cylinder is fixed and the other end is free. A 100 N-m torque is applied at the free end and the angle of twist of the free end is 0.5 o . Then total elastic strain energy stored in the cylinder is

Two rods of same dimensions are made of two materials A and B, whose stress-strain graphs are shown in the figure. The rods are subjected to axial tensile force. Then select the correct option.

For a perfectly rigid body (i) Young’s modulus is infinity (ii) Bulk modulus is zero (iii) Bulk modulus is infinity (iv) Compressibility is zero

If one end of a wire is fixed with a rigid support and the other end is stretched by a force of 10 N, then the increase in length is 0.5 mm. The ratio of the energy of the wire and the work done in displacing it through 1.5 mm by the weight is

The ratio of Young’s modulus of the material of two wires is 2 : 3. If the same stress is applied on both, then the ratio of elastic energy per unit volume will be

A 900 kg elevator hangs by a steel cable for which the allowable stress is 1.15 × 10 8 N / m 2 . What is the minimum diameter required if the elevator accelerates upward at 1.5 m / s 2 . Take g = 10 m / s 2

A long wire hangs vertically with its upper end clamped. A torque of 8 Nm applied to the free end twists it through 45 o . The potential energy of the twisted wire is

A small but heavy block of mass 10 kg is attached to a wire 0.3 m long. Its breaking stress is 4 .8 × 10 7 N / m 2 . The area of the cross section of the wire is 10 − 6 m 2 . The maximum angular velocity with which the block can be rotated in the horizontal circle is

Compressibility of water is 5 × 10 − 10 m 2 / N . Find the decrease in volume (in mL) of 100 mL of water when subjected to a pressure of 15 MPa.

The elasticity of invar

Which one of the following substances possesses the highest elasticity

Which one of the following quantities does not have the unit of force per unit area

Match the following columns and choose the correct option from the codes given below. Column I (A) Longitudinal stress (B) Shear stress (C) Volumetric stress (D) Tensile stress Column II (p) volume changes (q) shape changes (r) volume does not changes (s) shapes does not change

A wire of length L , area of cross-section A is hanging from a fixed support. The length of the wire changes to L ) when mass M is suspended from its free end. The expression for Young’s modulus is [NEET 2020]

The length of a metal wire is l 1 when the tension in it is T 1 and is l 2 when the tension is T 2 . The natural length of the wire is

The Young’s modulus of a rope of 10m length and having diameter of 2 cm is 20 x 10 11 dyne cm -2 . If the elongation produced in the rope is 1 cm, the force applied on the rope is

A steel ring of radius r and cross-sectional area A is fitted on to a wooden disc of radius R ( R > r ). If Young’s modulus of the steel is Y , then the force with which the steel ring is expanded is

Which of the following statement{s) is/are correct? I. The materials having low value of Young’s modulus of elasticity are more ductile. II. If Young’s modulus is less, then they can be easily stretched as wires.

A cable that can support a load w is cut into two equal parts. The maximum load that can be supported by either part is

A steel wire of cross-sectional area 3 × 10 − 8 m 2 can withstand a maximum strain of 10 -3 , Young’s modulus of steel is 2 × 10 11 Nm − 2 . The maximum mass this wire can hold is

The bulk modulus of a spherical object is B. If it is subjected to uniform pressure p, the fractional decrease in radius is

The Young’s modulus of a rope of 10m length and having diameter of 2 cm is 20 × 10 11 dyne cm -2 .If the elongation produced in the rope is 1 cm, the force applied on the rope is

The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?

A 5 cm cube has its upper face displaced by 0.2 cm by a tangential force of 8 N. The modulus of rigidity of the material of cube is

A bob of mass 10 kg is attached to a wire 0.3 m long. Its breaking stress is 4 . 8 × 10 7 N / m 2 . The area of cross-section of the wire is 10 – 6 m 2 . What is the maximum angular velocity with which it can be rotated in a horizontal circle?

The density of a metal at normal pressure is ρ . Its density when it is subjected to an excess pressure P is ρ ‘ . If B is Bulk modulus of the metal, the ratio of ρ ‘ ρ is :

A wire is elongated by 2 mm when a brick is suspended from it. When the brick is immersed in water, the wire contracts by 0.6 mm. What is the density of brick ?

The Young’s modulus of Brass and Steel are respectively 1 .0 × 10 10 N / m 2 and 2 × 10 10 N / m 2 . A Brass wire and a Steel wire of the same length are extended by 1mm under the same force, the radii of Brass and Steel wires are R B and R S . The relation between radii is?

A metal rod is subjected to tensile force and longitudinal strain produced in the rod is 0.02. If Poisson’s ratio of the metal is 0.3, the change produced in its volume is

A copper wire of cross sectional area A is under a tension F. Young’s modulus of copper is γ and Poisson’s ratio σ . Then find the fractional change in its cross sectional area.

Breaking stress of a metal is 10 8 N / m 2 and its density is 8 gm/c.c. Then what is is the maximum length of a rod made of this material that can be suspended from one end without breaking? Take g = 10 m / s 2

Two wires of the same material (Young’s modulus = Y) and same length L but radii R and 3R respectively are joined end to end and a weight w is suspended from the combination as shown in the figure. The elastic potential energy in the system is

A long thin metallic rod of length l , cross sectional area S and Young’s modulus γ rests on a smooth horizontal surface. A horizontal force P is applied at one end of the rod. Then the elongation produced in the rod is

The diagram shows variation between stress and change in length (x) of a wire at two different temperatures T 1 and T 2 , then

The approximate depth of an ocean is 2700 m. The compressibility of water is 45.4 × 10 –11 Pa –1 and density of water is 10 3 kg/m 3 . What fractional compression of water will be obtained at the bottom of the ocean?

A wire ‘AB’ is suspended about the end A. Marks C and D on it are 40 cm apart. When a load is suspended from B, then the marks C and D are displaced by 0.3 mm and 0.5 mm respectively. The original length of AD is

On loading a metal wire of cross section 10 –6 m 2 and length 2 m by a mass of 210 kg it extends by 16 mm and suddenly broke from the point of support. If density of that metal is 8000 kgm –3 and its specific heat is 420 Jkg –1 K –1 , the rise in temperature of wire is (g = 10 ms -2 )

Two blocks of masses 1 kg and 2kg are connected by a metal wire going over a smooth pulley as shown. The breaking stress of the metal is . If g = 10ms –2 . Then what should be the minimum radius of the wire used if it is not to break?

Select the correct alternative(s) a) Elastic forces are always conservative b) Elastic forces are not always conservative c) Elastic forces are conservative only when Hooke's law is obeyed d) Elastic forces may be conservative even when Hooke's law is not obeyed

A steel wire can support a maximum load of W before reaching its elastic limit. How much load can another wire, made out of identical steel, but with a radius one half the radius of the first wire, support before reaching its elastic limit?

The bulk modulus of water if its volume changes from 100 litre to 99.5 litre under a pressure of 100 atm is (Take 1 atm = 10 5 N m – 2 )

A wire is suspended vertically from a rigid support. When loaded with a steel weight in air, the wire extends by 16 cm. When the weight is completely immersed in water, the extension is reduced to 14 cm. The relative density of the material of the weight is

The area of a cross-section of steel wire is 0.1 cm 2 and Young’s modulus of steel is 2 × 10 11 N m – 2 . The force required to stretch by 0.1% of its length is

There is no change in the volume of a wire due to the change in its length on stretching. The Poisson’s ratio of the material of the wire is:

The lengths of an elastic wire are a, b when the tensions in it are 10 N, 20 N respectively. If the tension in the same wire is 40 N then its length is

A steel rod has a cross sectional area of 2 c m 2 . If the rod is subjected to a tensile force of 10 4 N and Young’s modulus of steel is 2 × 10 11 N / m 2 , what is the elastic potential energy stored per unit volume of the rod?

If one end of a wire is fixed with a rigid support and the other end is stretched by a force of 10N, then the increase in length is 0.5 mm. The ratio of the energy of the wire and the work done in displacing it through 1.5 mm by the weight is

A rubber ball is taken to a 100 m deep lake and its volume changes by 0.1 %. The bulk modulus of rubber is nearly:

Two rods of different materials having coefficients of thermal expansion α 1 and α 2 and Young’s moduli Y 1 and Y 2 respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature .There is no bending of the rods. If a1 and a2 are in the ratio 2 : 3, the thermal stresses developed in the two rods are equal provided Y 1 : Y 2 is equal to:

A wire fixed at the upper end stretches by length l by applying a force F. The work done in stretching is:

Consider the following statements. (A) Identical springs of steel and copper are equally stretched. More work will be done on the steel spring. (B) Steel is more elastic than copper. Select the correct option. (a)(A) is false, But (B) is true. (b) Both (A) and (B)are true. (c) (A) is true, But (B) is false. (d) Both (A) and (B)are false.

Consider the following statements. (A) Rigid body can be elastic. (B) If a force is applied on the rigid body, its dimension may change. Select the correct option. (a) (A) is false, But (B) is true. (b) Both (A) and (B) are true. (c) (A) is true, But (B) is false. (d) Both (A) and (B) are false.

A 0.1kg mass is suspended from a wire of negligible mass. The length of the wire is 1m and its cross sectional area is 4.9 × 10 − 7 m 2 . If the mass is pulled slightly in the vertically downward direction and then released, it performs simple harmonic motion of angular frequency 140 rad / s . Then the Young’s modulus of material of the wire is(Assume that the Hooke’s law is valid throughout the motion )

The stress versus strain graphs for wires of two materials A and B are as shown in the figure. lf Y A and Y B are the Young’s moduli of the materials, then

A wire of length L and radius r is rigidly fixed at one end. On stretching the other end of the wire with a force F, the increase in its length is l . If another wire of same material but of length 2L and radius 2r is stretched with a force of 2F, the increase in its length will be

A wire of cross-section A is stretched horizontally between two clamps located 2 l metre apart. A weight W kg is suspended from the mid point of the wire. If the mid pint sags vertically through a distance x < I. Find the Young’s modulus of the material and the value of extension x.

A material has normal density ρ and bulk modulus K. The increase in the density of the material when it is subjected to an external pressure P from all sides is

When a force is applied on a wire of uniform crosssectional area 3 x 10 – 6 m 2 and length 4 m, the increase in length is I mm. Energy stored in it will be (Y = 2 x 10 11 N / m 2 )

The upper end of a wire of radius 4 mm and length 100 cm is clamped and its other end is twisted through an angle of 30 ° . Then angle of shear is

If the volume of a wire remains constant when subjected to tensile stress, the value of Poisson’s ratio of the material of the wire is

A 5 m long aluminium wire (Y = 7 × 10 10 N / m 2 ) of diameter 3 mm supports a 40 kg mass. In order to have the same elongation in a copper wire ( Y = 12 × 10 10 N / m 2 ) of the same length under the same weight, the diameter should now be, in mm.

Young’s modulus of a rod is AgL 2 2 l for which elongation is λ due to its own weight when suspended from the ceiling. L is the length of the rod and A is a constant, which is:

The wires of same length and Young’s modulus are subjected to same tensile force. If ∆ l is the change in length of a wire, and c is the circumference of the wire, find the correct graph. The experiment is performed on the wires of different circumferences:

A lift is tied with thick iron and its mass is 314 kg. What should be the minimum diameter of wire if the maximum acceleration of lift is 1.2 m / sec 2 and the maximum safe stress of the wire is 1 x 10 7 N / m 2 ?

A thin rod AB of uniform cross sectional area is suspended from end A. If x be the elongation of the rod, then

The rod AB has a cross sectional area 5 mm 2 . Young’s modulus of its material is 2 × 10 10 N / m 2 . If mass of the rod is 10 Kg, strain produced at its mid point is

For a material, if the ratio of Young’s modulus of elasticity to the bulk modulus of elasticity is ¾, the ratio of young’s modulus of elasticity to modulus of rigidity will be

One face CD of a brass cube ABCD having length of side 10 cm is fixed and a tangential force is applied on the free face A. As a result the angular displacement of the other face is 0.18 o . If shear modulus of brass is 4 × 10 10 N / m 2 , the elastic potential energy stored in the cube is π 2 ≈ 10

A 2m long thin rod of mass 10 kg and cross sectional area 5 mm 2 is lying on a frictionless horizontal surface. A 1000 N force is applied to one end of the rod as shown in figure it young’s modulus of the rod is 2 × 10 11 N / m 2 , elongation produced in the rod is

A thin rod AB of length l, cross sectional area A and young’s modulus Y is acted upon by three forces as shown in figure. Then total elongation produced in the rod is [C is the mid point of the rod]

The compressibility of water is 4 × 10 − 5 per unit atmospheric pressure. The decrease in volume of 100 cm 3 of water, under a pressure of 100 atmosphere, will be

A steel ring of radius r and cross-section area A is fitted on to a wooden disc of radius R (R > r). If Young’s modulus be E, then the force with which the steel ring is expanded is

A rubber cord catapult has cross-sectional area 25 mm 2 and initial length of rubber cord is 10 cm. It is stretched to 5 cm and then released to project a missile of mass 5 gm. Taking Y rubber = 5 × 10 8 N / m 2 velocity of projected missile is

The strain-stress curves of three wires of different materials are shown in the figure. P, Q and R are the elastic limits of the wires. The figure shows that

The adjacent graph shows the extension ( Δl ) of a wire of length 1m suspended from the top of a roof at one end with a load W connected to the other end. If the cross-sectional area of the wire is 10 -6 m 2 , calculate the Young’s modulus of the material of the wire.

One end of uniform wire of length L and of weight W is attached rigidly to a point in the roof and a weight W 1 is suspended from its lower end. If s is the area of cross section of the wire, the stress in the wire at a height (3L/4) from its lower end is

Two blocks of masses I kg and 2 kg are connected by a metal wire going over a smooth pulley as shown in the figure. The breaking stress of the metal is 40 3 π × 10 6 N / m 2 .If g = 10 ms − 2 , then what should be the minimum radius of the wire used if it is not to break?

The work per unit volume to stretch the length by 1% of a wire with cross sectional area of 1 mm 2 will be. Y = 9 × 10 11 N / m 2

The elastic limit of an elevator cable is 2 × 10 9 N / m 2 . The maximum upward acceleration that an elevator of mass 2 × 10 3 kg can have when supported by a cable whose cross-sectional area is 10 − 4 m 2 provided the stress in cable would not exceed half of the elastic limit would be

A 5-kg rod of square cross section 5 cm on a side and 1 m long is pulled along a smooth horizontal surface by a force applied at one end. The rod has a constant acceleration of 2 ms − 2 . Determine the elongation in the rod. (Young’s modulus of the material of the rod is 5 × 10 9 N / m 2 ).

The bar shown in the figure is made of a single piece of material. It is fixed at one end. It consists of two segments of equal length L/2 each but different cross-sectional area A and 2A.Find the ratio of total elongation in the bar to the elongation produced in thicker segment under the action of an axial force F. Consider the shape of joint to remain circular. (Given: Y is Young’s modulus).

Two steel wires of same length but radii r and 2r are connected together end to end and tied to a wall as shown. The force stretches the combination by 10 mm. How far does the midpoint A move (in mm)?

Steel and copper wires of same length are stretched by the same weight one after the other. Young’s modulus of steel and copper are 2 × 10 11 N / m 2 and 1 .2 × 10 11 N / m 2 . The ratio of increase in length

The temperature of a wire of length 1 metre and area of cross-section 1 c m 2 is increased from 0°C to 100°C. If the rod is not allowed to increase in length, the force required will be ( α = 10 − 5 / ° C and Y = 10 11 N / m 2 )

Increase in length of a wire is 1 mm when suspended by a weight. If the same weight is suspended on a wire of double its length and double its radius, the increase in length will be

A rod of length l and area of cross-section A is heated from 0°C to 100°C. The rod is so placed that it is not allowed to increase in length, then the force developed is proportional to

If the density of the material increases, the value of Young’s modulus

In steel, the Young’s modulus and the strain at the breaking point are 2 × 10 11 Nm − 2 and 0.15 respectively. The stress at the breaking point for steel is therefore

An Indian rubber cord L metre long and area of cross-section A metre 2 is suspended vertically. Density of rubber is p kg/metre 3 and Young’s modulus of rubber is Y newton/metre 2 . If the cord extends by l metre under its own weight, then extension I is

A nylon rope 3 cm in diameter has a breaking strength of 1.5 X 10 5 N. The breaking strength of a similar rope 1.5 cm in diameter is

A thick copper rope of density l.5 x 10 3 kg/m 3 and Young’s modulus 5 x 10 6 N/m 2 , 8 m in length when hung hom the ceiling of a room, the increase in its length due to its own weight is

A wire elongates by l mm when a load w is hanged from it. If the wire goes over a pulley and two weights w each are hung at the two ends, the elongation of the wire will be (in mm)

The ratio of lateral contractional strain and the longitudinal elongational strain of a stretched wire is

A wire of area of cross-section 3.0mm 2 and natural length 50 cm is fixed at one end and a mass of 2.1 kg is hung from the other end. Young’s modulus of the material of wire is 1.9 x 10 11 N / m 2 . Take g =10m / s 2 . The potential energy stored in the wire in steady state will be

A wire of length /and cross-sectional area A is made of a material of Young’s modulus Y. If the wire is stretched by an amount x, the work done is

Two blocks of masses 1 kg and 2 k8 are connected by a metal wire going over a smooth pulley as shown in fig. The breaking stress of the metal is 2 × 10 9 N / m 2 .If the wire is not to break, its minimum radius should be

Two springs of equal lengths and equal cross-sectional area are made of material whose Young’s modulii are in the ratio of 2 : 3. They are suspended and loaded with the same mass. When stretched and released, they will oscillate with time periods in the ratio of

A metallic rod breaks when strain produced is 0.2%.The Young’s modulus of the material of the rod is 7x l0 9 N/m 2 . What should be its area of cross-section to support a load of 10 4 N ?

A 20 N stone is suspended from a wire and its length changes by 1%. If the Young’s modulus of the material of the wire is 2 x 10 11 N /m 2 , the area of cross-section of the wire is

The Young’s modulus of brass and steel are respectively 10 x 10 10 N ,/ m 2 and z x 10 10 N / m 2. A brass wire and a steel wire of the same length are extended by 1 mm under the same force, the radii of brass and steel wires are R B and R s respectively. Then

A light rod of length 200 cm is suspended from the ceiling horizontally by means of two vertical wires of equal length tied to its ends. One of the wires is made of steel and is of cross-section 0.1cm 2 and the other of brass of cross section 0.2cm 2 . Along the rod at which distance a weight may be hung to produce equal stresses in both the wires ?

An iron rod Y = 10 11 N / m 2 , α = 10 − 5 / ∘ C has a length of one metre and cross-section 10cm 2 . By raising its temperature from 0°c to 100°C and holding it so that it is not permitted to expand or bend, the force developed is

Two bodies of masses 1 kg and 2 kg are connected by a metal wire as shown in fig. A force of10 Nis applied on the body of mass 2 kg. The breaking stress of metal wire is 2 x 10 9 N/m 2 . What should be the minimum radius of the wire used, if it is not to break ?

The Young’s modulus of a wire is numerically equal to the stress which will

When a pressure of 100 atm is applied on a spherical ball, then its volume reduces to 0.01%. The bulk modulus of the material of the rubber (in dyne cm -2 ) is

One end of a uniform wire of length L and weight ω is attached rigidly to a point in roof and a weight ω 1 is suspended from its lower end. If S is the area of cross-section of the wire, the stress in the wire at a height of 3 L 4 from its lower end is

The graph shown below gives the extension ( Δ L) of a wire of length 1 m suspended from the top of a roof at one end with a load w connected to the other end. If the cross-sectional area of the wire is 10 -6 m 2 , calculate the Young’s modulus of the material of the wire.

A uniform cylindrical rod of length L and cross-sectional area A having Young’s modulus Y is acted upon by forces as shown in figure. [CG PMT 2015] The elongation produced in the rod is

A load of 4 kg is suspended from a ceiling through a steel wire of length 2 m and radius 2 mm. It is found that, the length of the wire increases by 0.031 mm as equilibrium is achieved. What would be the Young’s modulus of steel? (Take, g = 3.l π ms -2 )

A uniform wire of cross-sectional area A and Young’s modulus Y is stretched within the elastic limit. If S is the stress in the wire, the elastic energy density stored in the wire in terms of the given parameters is

The temperature of a wire is doubled. The Young’s modulus of elasticity

The load versus elongation graph for four wires of the same material and same length is shown in the figure. The thickest wire is represented by the line

When a pressure of 100 atm is applied on a spherical ball, then its volume reduces to 0.01%. The bulk modulus of the material of the rubber (in dyne cm 2 ) is

Two block of masses of 1 kg and 2 kg are connected by a metal wire going over a smooth pulley. The breaking stress of metal is 40 3 π × 10 6 Nm − 2 .What should be the minimum radius of wire used, if it should not break? Take, g = 10 ms − 2

A thick rope of rubber of length 8 m and density 1.5 × 10 3 kgm − 3 has Young’s modulus 5 × 10 6 Nm − 2 . When hung from ceiling of a room, the increase in length due to its own weight is

The length of a metal wire is l 1 when the tension in it is T 1 and is l 2 when the tension is T 2 . The natural length of the wire is

Wires A and B are made from the same material. A has twice the diameter and three times the length of B. If the elastic limits are not reached, when each is stretched by the same tension, the ratio of energy stored in A to that in B is

Theoretically, the value of Poisson’s ratio σ lies between

A uniform cube is subjected to volume compression. If each side is decreased by 1%, then bulk strain is

If the displacement (x) and velocity (v) of a particle executing simple harmonic motion are related through the expression 4 v 2 = 25 – x 2 , then its time period is

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A . If the length of the first wire is increased by ∆ l on applying a force F , how much force is needed to stretch the second wire by the same amount?

A 900 kg elevator hangs by a steel cable for which the allowable stress is 1 .15 × 10 8 N / m 2 . What is the minimum diameter required if the elevator accelerates upward at 1 .5 m / s 2 . Take g= 10 m / s 2

Copper of fixed volume V is drawn into wire of length ι . When this wire is subjected to a constant force F, the extension produced in the wire is ∆ ι . Which of the following graphs is a straight line?

Maximum stress that can be applied to a wire which supports an elevator is σ . Mass of elevator is m and it is moved upwards with an acceleration of g 2 . Minimum diameter of wire (Neglecting weight of wire) must be

A block of gelatin is 60 mm by 60 mm by 20 mm when unstressed. A force of 0.245N is applied tangentially to the upper surface , causing a 5 mm displacement relative to the lower surface. Following observations are made regarding the block. (i) the shearing stress developed on the surface is 68.1 Pa (ii) the shearing strain developed on surface is 0.25 Pa (iii) the shear modulus of material is 272.4 N / m 2 Regarding above statements we can say

When a block of mass M is suspended by a long wire of length L, the length of the wire becomes (L+l). The elastic potential energy stored in the extended wire is

A substance breaks down under a stress of 10 5 Pa. If the density of the substance is 2 × 10 3 Kg / m 3 , find the minimum length of the wire made of this substance which will break under its own weight (g= 10 m / s 2 )

The Young’s modulus of steel is twice that of brass. Two wires of same length and of same area of cross section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of

If the one end of a wire is fixed with a rigid support and the other end is stretched by a force of 10N, then the increase in length is 0.5mm. The ratio of the energy of the wire and the work done in displacing it through 0.5 mm by the same force

If the ratio of diameters, lengths and Young’s modulus of steel and copper wires shown in the figure are p, q and s respectively, then the corresponding ratio of increase in their lengths would be

The bulk modulus of a spherical object is ‘B’. If it is subjected to uniform pressure ‘p’, the fractional decrease in radius is

A wire of length L, area of cross section A is hanging from a fixed support. The length of the wire changes to L 1 when mass M is suspended from its free end. The expression for Young’s modulus is

A body of mass ‘m’ is attached to the lower end of a metal wire, whose upper end is fixed. If the elongation in the wire is ‘l ’, the correct choices of the following are a) Loss in potential energy of mass is mgl b) Elastic potential energy stored in the wire is m g l 2 c) Elastic potential energy stored in the wire is mgl d) Heat produced is m g l 2

The elongation in a metallic rod hinged at one end and rotating in a horizontal plane becomes four times of the initial value. The angular velocity of rotation becomes

Elongation of a wire under its own weight is ‘e’. Another wire of half the length but double the density and Young’s modulus elongates due to its own weight by an amount of

A steel ring of radius r and cross section a is fitted onto a wooden disc of radius R ( R > r ). If the Young’s modulus be E, then the force with which the steel ring is expanded is

The stress-strain curves are drawn for two different materials X and Y. It is observed that the ultimate strength point and the fracture point are close to each other for material X but are far apart for material Y. We can say that materials X and Y are likely to be (respectively),

Young’s modulus of the material of a rod is ‘Y’ and its breaking stress is ‘ σ ‘ . If density of the rod is ‘ ρ ’, The maximum length of a rod that can be suspended from one end is

A long metallic string of mass m, length l , cross –sectional area A and Young’s modulus Y is suspended from one end A. A small object of mass 2m is attached to its lower end B. Then elongation produced in the string is

Two rods of different materials having coefficients of linear expansion a1 and a2 and Young’s moduli, Y 1 and Y 2 , respectively, are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If α 1 / α 2 = 2/3, then the thermal stresses developed in the two rods are equal, provided Y 1 / Y 2 is equal to

If Poisson’s ration ( μ ) of a substance is 0.4, The relation between Bulk modulus of elasticity (k) and modulus of rigidity η is

Strain energy B stored in unit volume of a rod of diameter ‘d’, subjected to tensile force is ‘u’. Then the strain energy stored in unit volume of a rod of diameter ‘2d’, made of same material and subjected to same tensile force, will be

The elastic limit of an elevator cable is 2 × 10 9 N/ m 2 . The maximum upward acceleration that an elevator of mass 2 × 10 3 kg can have when supported by a cable whose cross-sectional area is 10 – 4 m 2 , provided the stress in cable would not exceed half of the elastic limit would be

One end of a long metallic wire of length L is tied to the ceiling. The other end is tied to a mass less spring of spring constant K. A mass m hangs freely from the free end of the spring. The area of cross-section and the Young’s modulus of the wire are A and Y respectively. Find the time period with which mass m will oscillate if it is slightly pulled down and released

A block of mass M is suspended from a wire of length L area of cross section A and young’s modulus Y. The elastic potential energy stored in the wire is

A wire is stretched 1 mm by a force of 1 kN. How far would a wire of the same material and length but of four times that diameter be stretched by the same force?

The compressibility of a material is

A rod of circular cross section has a length ‘ l ’ and radius ‘r’. It is subjected to a tensile force and the total elastic potential energy stored in the rod is U. If another rod of length 2l and radius 2r is subjected to same tensile force, Then elastic potential energy stored in the rod will be

If Poisson’s ratio of a material is 0.3, the ratio of its bulk modulus of elasticity of modulus of rigidity is

A cube is shifted to a depth of 100 m in a lake. The change in volume is 0.1% the bulk modulus of the material is nearly

Two wires of same material have lengths l and 2 l . Their radii are in the ratio 1 : 2. The wires are stretched by the same force. If elongation produced in the second wire is 1 mm, then elongation in the first wire will be

A long steel rod of uniform cross sectional area is suspended from one end. If x be the elongation of lower half of the rod, the elongation of upper half is

Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is 1:4, the ratio of their diameters is

A cube of metal is subjected to a hydrostatic pressure of 4 GPa. The percentage change in the length of the side of the cube is close to : (Given bulk modulus of metal, B = 8 × 10 10 Pa)

Two wires of diameter 0.25cm. One made of steel and the other made of brass are loaded as shown in figure. The length of steel wire 1.5m and that of brass is 1.0m. The elongation in steel wire is (10 -4 m) ( Y steel = 2.0 × 10 11 Pa, Y brass = 0.91 × 10 11 Pa)

Each of three blocks shown in figure has a mass 3kg. The wire connecting, blocks A and B has area of cross-section 0.005 cm 2 and Young's modulus of elasticity Y = 2×10 11 N/m 2 . Neglect friction. Find the elastic potential energy stored per unit volume in wire connecting blocks A and B in steady state (in j/m 3 take g = 10m/s 2 )

The ratio of diameters of two wires, made of same material is 2:1. The ratio of their lengths is 1:2. On applying the same tensile force to the wires, the ratio of elastic potential energies stored in the wires will be

The Young’s modulus of a wire of length L and radius r is Y. If the length is reduced to L 2 and radius r 2 then the Young’s modulus will be

Assertion: Bulk modulus of elasticity (K) represents incompressibility of the material Reason : Bulk modulus of elasticity is proportional to change in pressure.

Assertion : Bulk modulus of elasticity B represents incompressibility of the material. Reason : B = ∆ P – ∆ V V , where symbols have their usual meaning.

Statement I : The compressibility of solids is less than that of gases and liquids. Statement II : There is tight coupling between the neighbouring atoms in solids.

Statement I : Strain is a unitless quantity Statement II : Strain is equivalent to force.

Statement I : Glassy solids have sharp melting point. Statement II : The bonds between the atoms of glassy solids get broken at the melting point.

Statement I : The stress-strain behaviour varies from material to material. Statement II : A rubber can be pulled to several times its original length and still returns to its original shape.

A cord of mass m, length L, area of cross-section. A and Young’s modulus y is hanging from a ceiling with the help of a rigid support. The elongation developed in the wire due to its own weight is

One end of a uniform wire of length L and of weight W is attached rigidly to a point in the roof and a weight W 1 is suspended from its lower end. If S is the area of cross-section of the wire, the stress in the wire at a height 3 L 4 from its lower end is

The radii and Young’s moduli of two uniform wires A and B are in the ratio 2 : 1 and 1 : 2 respectively. Both wires are subjected to the same longitudinal force. If the increase in length of the wire A is one percent, the percentage increase in length of the wire B is

When a wire of uniform cross-sectional area, length l and density ρ is suspended from one end, its elongation is found to be x. Then Young’s modulus of its material is

A block of mass m is tied to one end of a string of length l, young’s modulus Y and cross-sectional area A. The block is made to rotate in a horizontal circle of radius l with angular velocity ω in a gravity free space. If elongation of the wire is x, then elastic potential energy stored in the wire is

Match the column I with column II Column-I Column-II (i) The shape of rubber heel changes under stress (p) Young’s modulus of elasticity is involved (ii) In a suspended bridge, there is a strain in the ropes by the load of the bridge (q) Bulk modulus of elasticity is involved (iii) In an automobile tyre, when air is compressed, the shape of tyre changes r) Modulus of rigidity is involved (iv) A solid body is subjected to a deforming force. (s) All the modulli of elasticity are involved Now mark the correct choice from the codes given below. Codes

A cord of mass m, length L, area of cross-section A and Young’s modulus y is hanging from a ceiling with the help of a rigid support. The elongation developed in the wire due to its own weight is

A sphere contracts in volume by 0.01%, when taken to the bottom of sea 1 km deep. The bulk modulus of the material of the sphere is (Given density of sea water may be taken as 1.0 × 10 3 kg m – 3 )

A steel cable with a radius 2 cm supports a chairlift at a ski area. If the maximum stress is not to exceed 10 8 N m – 2 , the maximum load the cable can support is

The Young’s modulus of steel is twice that of brass. Two wires of the same length and of the same area of cross section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights addded to the steel and brass wires must be in the ratio of

The approximate depth of an ocean is 2700 m. The compressibility of water is 45 . 4 × 10 – 11 Pa – 1 and density of water is 10 3 kg / m 3 . What fractional compression of water will be obtained at the bottom of the ocean?

Copper of fixed volume V is drawn into wire of length l. When this wire is subjected to a constant force F, the extension produced in the wire is ∆ l . Which of the following graphs is a straight line?

A rubber rope of length 8 m is hung from the ceiling of a room. What is the increase in length of rope due to its own weight? (Young’s modulus of elasticity of rubber = 5 × 10 6 Nm – 2 and density of rubber = 1 . 5 × 10 3 kg m – 3 . Take g = 10 ms – 2 )

Two strips of metal are riveted together at their ends by four rivets, each of diameter 6 mm. Assume that each rivet is to carry one quarter of the load. If the shearing stress on the river is not to exceed 6 . 9 × 10 7 P a , the maximum tension that can be exerted by the riveted strip is

A 40 kg boy whose leg are 4 cm 2 in area and 50 cm long falls through a height of 2 m without breaking his leg bones. If the bones can stand a stress of 1 . 0 × 10 8 N / m 2 , calculate the Young’s modulus for the material of the bone.

If a pressure ‘p’ is applied normal to a wire of Young’s modulus Y, the energy stored per unit volume is:

A long elastic spring is stretched by 2 cm and its potential energy is U. If the spring is stretched by 10 cm, the P.E., will be:

If Poisson’s ratio of a material is 0.4, the ratio of its young’s modulus to Bulk modulus of elasticity is

A metallic rod, having uniform cross-sectional area of 2 c m 2 is subjected to a tensile force of 200 KN. If young’s modulus of the metal is 2 × 10 6 N / c m 2 , find the strain produced in the rod.

The ratio of young’s modulus of elasticity (Y) to the bulk modulus of elasticity of a material is 1.8. If the length of a rod of uniform cross sectional area made of thin material is increased by 0.04% under the action of a tensile force, then its diameter changes by

Density of a material is 8 g m / c m 3 . 1 Km long wire, made of this material is suspended from a helicopter. Then maximum stress developed in the wire is (Take g = 10 m / s 2 )

The density of water at the surface of ocean is ρ . If the bulk modulus of water is B, then the density of ocean water at depth, when the pressure is α p 0 where p 0 is the atmospheric pressure, is

Which of the following is most elastic in the language of physics?

A bar of iron of length 1 m and 1 cm 2 cross-section is heated from 0 °C to 100°C. The coefficient of linear expansion of iron is 10 -5 l°C. The increase in its length is:

A wire ( Y = 2 x 10 11 N/m 2 ) has length I m and area 1 mm 2 ; the work required to increase its length by 2 mm is:

Two wires are made of the same material and have the same volume. However wire l has cross-sectional area A and wire 2 has cross-sectional area 3A. If the length of wire 1 increases by ∆ x . on applying force F, how much force is needed to Stretch wire 2 by the same amount?

For a constant hydraulic stress on an object, the fractional change in the object’s volume ∆ V V and its bulk modulus (B) are related as:

Which of the following relations is correct connecting the elastic constants?

A beam of metal supported at the two ends is loaded at the centre. The depression at the centre is proportional to:

Young’s modulus of a wire of length land radius r is Y. Length of the wire is reduced to l 2 and radius also reduced to r 2 .Young’s modulus will now be

Breaking stress of a material is 10 6 N/m 2 . If the density of material is 3 x 10 3 kg/m 3 , what should be the length of this material of uniform cross-section so that it breaks by its own weight? (take g = 10 m/s 2 )

Bulk modulus of water is 2 x 10 9 N/m 2 . Change in pressure required to increase density of water by 0.1 % is:

Normal density of gold is p and its bulk modulus is K. Increase in density of a lump of gold when a pressure P is applied uniformly on all sides is:

A body of mass 10 kg is attached to a wire of length 0.3 m. Its breaking stress is 4.8 x 10 7 N/m 2 . Area of cross-section of the wire is 10 -6 m 2 . What is the maximum angular velocity with which it can be rotated in a horizontal circle?

One end of a uniform wire of length L and of weight W is attached rigidly to a point in the roof and a weight W1 is suspended from its lower end. If Sis the area of cross- section of the wire, the stress in the wire at a height (3L/4) from its lower end is:

Two wires of same material and radius have their lengths in ratio 1 : 2. If these wires are stretched by the same force, the strain produced in the two wires will be in the ratio:

A wire elongates by / mm when a load Wis hanged from it. If the wire goes over a pulley and two weights W each are hung at the two ends, the elongation of the wire will be (in mm):

A uniform rod of mass m, length L, area of cross-section A and Young’s modulus Y hangs from a rigid support. Its elongation due to its own weight will be:

Young’s modulus of iron is 2 x 10 11 N/m 2 and interatomic spacing in iron is 3 x 10 -10 m. Interatomic force constant is:

The Poisson’s ratio of a material is 0.5. If a force is applied to a wire of this material, there is a decrease in the cross-sectional area by 4%. The percentage increase in the length is:

A wire of length L and radius a rigidly fixed at one end. On stretching the other end of the wire with a force F, the increase in its length.is /. If another wire of same material but of length 2L and radius 2a is stretched with a force 2F, the increase in its length will be:

Regarding elasticity which of the following statements are correct? (i) Rubber does not obey Hooke’s law. (ii) Elasticity* can be different for tensile and compressive stress. (iii) Elasticity is independent of temperature . (iv) Poisson’s ratio is a modulus of elasticity.

A copper wire and a steel wire of the same diameter and length are joined end to end and a force is applied which stretches their combined length by 1 cm. Then the two wires will have:

A wire is suspended from the ceiling and stretched under the action of a weight F suspended from its other end. The force exerted by the ceiling on it is equal and opposite to the weight. (i) Tensile stress at any cross-section A of the wire is F A . (ii) Tensile stress at any cross-section is zero. (iii) Tensile stress at any cross-section A of the Wire is 2 F A . (iv) Tension at any cross-section A of the wire is F.

For an ideal liquid (i) the bulk modulus is infinite. (ii) the bulk modulus is zero. (iii) the shear modulus is infinite. (iv) the shear modulus is zero.

The Young’s modulus of steel is twice that of brass. Two wires of same length and of same area of cross-section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of :

A rod of length land negligible mass is suspended at its two ends by two wires of steel (wire A) and aluminium (wire B) of equal lengths Fig. The cross-sectional areas of wires A and Bare 1.0 mm 2 and 2.0 mm 2 , respectively. ( Y Al = 70 x 10 9 Nm – 2 and Y steel = 200 X 10 9 Nm – 2 ) (i) Mass m should· be suspended close to wire A to have equal stresses in both the wires. (ii) Mass m should be suspended close to wire B to have equal stresses in both the wires. (iii) Mass m should be suspended at the middle of the wires to have equal stresses in both the wires. (iv) Mass m should be suspended close to wire A to have equal strains in both the wires.

A string of length ‘/’ and radius ‘a’ is stretched between two fixed points A and B without tension. The middle point of the string is pulled to a small distance ‘d’ in a direction, perpendicular to the original length of the string. If the Young’s modulus of the material of the string is Y, the energy stored in the string is:

The approximate depth of an ocean is 2700 m. The compressibility of water is 45.4 x 10 -11 Pa -1 and density of water is 10 3 kg/m 3 . What fractional compression of water will be obtained at the bottom of the ocean?

The bulk modulus of a spherical object is ‘B ‘. If it is subjected to uniform pressure ‘ p ‘, the fractional decrease in radius is :

The diagram shows a force-extension graph for a rubber band. Consider the following statements : I. It will be easier to compress this rubber than expand it. II. Rubber does not return to its original length after it is stretched. Ill. The rubber band will get heated if it is stretched and released. Which of these can deduced from the graph?

Copper of fixed volume’ V’; is drawn into wire of length’ l’. When this wire is subjected to a constant force ‘F’, the extension produced in the wire is ‘ ∆ l ‘. Which of the following graphs is a straight line?

The graph shown the extension of wire of length 1 m suspended from the top of a roof at one end and with a load W connected to the other end. If the cross sectional area of the wire is 1 mm 2 , then the Young’s modulus of the material of the wire is

If there is no change in the volume of wire on stretching, then Poisson’s ratio for the material of wire is:

Consider the following statements. (A) Stress is the internal restoring force per unit area of a body. (B) Rubber is more elastic than brass. Select the correct option. (a)(A) is false, But (B) is true. (b) Both (A) and (B)are true. (c) (A) is true, But (B) is false. (d) Both (A)and(B)are false.

Consider the following statements. (A) Spring is made of steel and not of copper. (B) Steel is more elastic than copper. Select the correct option. (a)(A) is false, But (B) is true. (b) Both (A) and (B)are true. (c) (A) is true, But (B) is false. (d) Both (A) and (B)are false.

Consider the following statements. (A) Spring balances show wrong readings after they had been used for a long time. (B) On using for long time, spring balances loses its elastic strength. Select the correct option. (a)(A) is false, But (B) is true. (b) Both (A) and (B)are true. (c) (A) is true, But (B) is false. (d) Both (A) and (B)are false.

Consider the following statements. (A) A material having greater Young’s modulus also possesses greater bulk modulus. (B) The elastic moduli are due to inter moleculer forces existing in the mater

Fig. shows the change x in the length of a thin uniform wire caused by the application of stress F at two different temperatures T 1 and T 2 . The variations shown suggest that:

If a bar is made of · copper whose coefficient of linear expansion is one and a half times that of iron, the ratio of force developed in the copper bar to the iron bar of identical lengths and cross-sections, when heated through the same temperature range (Young’s modulus of copper may be taken to be equal to that of iron) is:

A wire suspended vertically from one of its ends is stretched by attaching a weight of 200 N to the lower end. The weight stretches the wire by 1 mm. Then the elastic energy stored in the wire is:

Increase in length of a wire on stretching is 0.025%. If its poisson’s ratio is 0.4, percentage decrease in diameter is:

A wire is stretched by hanging a weight from its end and develops a longitudinal strain σ 1 , Y being the Young’s modulus, elastic potential energy of the wire per unit volume can be expressed as:

A cube at temperature 0°C is compressed equally from all sides by an external pressure P. By what amount should its temperature be raised to bring it back to the size it had before the external pressure was applied? Bulk modulus of material of cube is K and the coefficient of linear expansion is α .

An aluminium and steel wires of same length and cross-section are attached end to end. The compound wire is hung from a rigid support and a load is suspended from the free end. Y of steel is ( 20/7) times of aluminium. The ratio of increase of length of steel wire to aluminium wire is:

When a wire is stretched to double its length: (i) its radius is halved (ii) strain is unity (iii) stress is equal to Young’s modulus (iv) Young’s modulus is equal to twice the elastic energy per unit volume

Consider the following statements. (A) Steel is more elastic than rubber. (B) Under given deforming force, steel is deformed less than rubber. Select the correct option. (a) (A) is false, But (B) is true. (b) Both (A) and (B)are true. (c) (A) is true, But (B) is false. (d) Both (A)and(B)are false.

Two wires A and B have the same cross-section and are made of the same material, but the length of wire A is twice that of B. Then for a give load.

A student performs an experiment to determine the Young’s modulus of a wire, exactly 2m long, by Searle’s method. In a particular reading, the student measures the extension in the length of the wire to be 0.8mm with an uncertainty of ± 0.05 mm at a load of exactly 1.0kg. The student also measures the diameter of the wire to be 0.4mm with an uncertainty of ± 0.01 mm . Take g = 9.8 m / s 2 (exact). The Young’s modulus obtained from the reading is[ Take π = 3.14 ]

A thin uniform elastic rod of natural length l, area of cross-section A, density ρ and young’s modulus Y is just completely immersed in vertical position in a liquid of density 2 ρ by applying a force F in vertically downward direction as shown. What is the compression in the rod?

The bar shown in the figure is made of a single piece of material. It is fixed at one end. It consists of two segments of equal length L/2 each but different cross-sectional area A and 2A. Find the ratio of total elongation in the bar to the elongation produced in thicker segment under the action of an axial force F. Consider the shape of joint to remain circular. (Given: Y is Young’s modulus).

The mass and length of a wire are M and L respectively. The density of the material of the wire is d. On applying the force F on the wire, the increase in length is l, then the Young’s modulus of the material of the wire will be

A wire of length L and cross-section ‘A’ has Young’s modulus of material Y. It is stretched by an amount ‘x’. The work done against restoring force is

The dimensions of four wires of the same material are given below. In which wire the increase in length will be maximum when the same tension is applied

A steel wire of length 4.5 m and cross-sectional area 3 x 10 – 5 m 2 stretches by the same amount as a copper wire of length 3.5 m and cross sectional area of 4 × 10 – 5 m 2 under a given load. The ratio of the Young’s modulus of steel to that of copper is

Steel and copper wires of same length and area are stretched by the same weight one after the other. Young’s modulus of steel and copper are 2 × 10 11 N / m 2 and 1 . 2 × 10 11 N / m 2 . The ratio of increase in length is

A concrete sphere of radius R has a cavity of radius r which is packed with sawdust. The specific gravities of concrete and sawdust are respectively 2.4 and 0.3 for this sphere to float with its entire volume submerged under water. Ratio of mass of concrete to mass of sawdust will be

The diagram shows stress v/s strain curve for the materials A and B. From the curves we infer that

When load of 5 kg is hung on a wire then extension of 3 m takes place, then work done will be

If a spring extends by x on loading, then the energy stored by the spring is (if T is tension in the spring and k is spring constant)

When a block of mass M is suspended by a long wire of length L, the length of the wire becomes (L + l ). The elastic potential energy stored in the extended wire is

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. lf the length of the first wire is increased by ∆ l on applying a force F, how much force is needed to stretch the second wire by the same amount ?

The bulk modulus of a spherical object is ‘B’. If it is subjected to uniform pressure ‘p’ , the fractional decrease in radius is

Statement I: The materials which have very small range of plastic extension are called brittle materials. Statement II: If the stress is increased beyond the elastic limit, the material will break.

A bar of cross-sectional area A is subjected to equal and opposite tensile forces at its ends. Consider a plane section (PS) of the bar, whose normal makes an angle ϕ with the axis (axis is along the length) of the bar. Column-I Column-II i. shearing stress on PS p. F A cos 2 ϕ ii. tensile stress on PS q. 0° iii. the tensile stress is maximum for ϕ = r. F A sinϕ cosϕ iv. the shearing stress is maximum for ϕ = s. 60° t. 45° Match the given columns and select the correct option from the codes given below. Codes

Consider the following statements: (i) Young’s modulus is numerically equal to the stress which will double the length of a wire. (ii) Viscosity of gases is greater than that of liquids. (iii) The surface tension of a liquid decreases due to the presence of insoluble contamination. The number of above statements that are true is

The elongation in a metallic rod hinged at one end and rotating in a horizontal plane becomes four times of the initial value. The angular velocity of rotation becomes

A wire of cross-section A is stretched horizontally between two clamps located 2l metre apart. A weight W kg is suspended from the mid point of the wire. If the mid pint sags vertically through a distance x < I the strain produced is:

When the tension in a metal wire is T 1 , its length is l 1 . When the tension is T 2 , its length is l 2 .The natural length of wire is

Assuming that shear stress at the base of a mountain is equal to the force per unit area due to its weight. Calculate the maximum possible height of a mountain on the earth if breaking stress of a typical rock is 3 × 10 8 Nm – 3 and its density is 3 × 10 3 kg m – 3 . (Take g = 10 ms – 2 )

A stone of mass m tied to one end of a wire of length L. The diameter of the wire is D and it is suspended vertically. The stone is now rotated in a horizontal plane and makes an angle 6 with the vertical. If Young’s modulus of the wire is Y, then the increase in the length of the wire is

A metal cylinder of length L is subjected to a uniform compressive force F as shown in the figure. The material of the cylinder has Young’s modulus Y and Poisson’s ratio σ . The change in volume of the cylinder is

Wires A and B are connected with blocks P and Q as shown. The ratio of lengths, radii and Young’s modulus of wires A and B are r:1, 1:2r and 1:3r respectively (r is a constant). Find the mass of block P if ratio of increase in their corresponding lengths is 1 6 r 2 . The mass of the block Q is 3M.

If the ratio of lengths, radii and Young’s moduli of steel and brass wires in the figure are a, b and c respectively, then the corresponding ratio of increase in their lengths is

A light rod of length 2 m is suspended from the ceiling horizontally by means of two vertical wires of equal length tied to its end. One of the wires is made of steel and is of cross-section 0.1 cm 2 . The other wire is of brass of cross-section 0.2 cm 2 . A weight is suspended from a certain point of the rod such that equal stresses are produced in both the wires. The rod remains horizontal in this case also. Find out the position of the load from the steel wire.

The forces responsible for a body regaining its shape after removal of deforming forces are

The force (F)-extension ( λ ), graph shows that the strain energy stored in the material under test, for an extension of 4 mm, is greater than which of the following values?

A rubber of volume 2000 cc is alternately subjected to tension and released. The figure shows the stress-strain curve of rubber. Each curve is a quadrant of an ellipse. The amount of energy lost as heat per cycle per unit volume will be

The elastic energy per unit volume in terms of longitudinal strain σ and Young’s modulus Y is:

The work per unit volume to stretch the length by 1% of a wire with cross sectional area of 1 mm 2 will be. [ Y = 9 × 10 11 N / m 2 ]

A smooth uniform string of natural length L 0 , cross sectional area A and Young’s modulus Y is pulled along its length by a force F on a horizontal smooth surface. The elastic potential energy stored in the string is

The length of a rod is 20 cm and area of cross-section 2 cm 2 . The Young’s modulus of the material of wire is 1 . 4 × 10 11 N / m 2 . If the rod is compressed by 5 kg-wt along its length, then increase in the energy of the rod in joules will be

K is the force constant of a spring. The work done in increasing its extension from l 1 to l 2 will be

Wires A and B are made from the same material. A has twice the diameter and thee times the length of B. If the elastic limits are not reached, when each is stretched by the same tension, the ratio of energy stored in A to that in B is

If the potential energy of a spring is V on stretching it by 2 cm, then its potential energy when it is stretched by 10 cm will be

Two wires of same diameter of the same material having the length l and 2l. If the force f is applied on each, the ratio of the work done in the two wires will be

A brass rod of cross-sectional area I cm 2 and length 0.2 m is compressed lengthwise by a weight of 5 kg. If Young’s modulus of elasticity of brass is 1 × 10 11 N / m 2 and g = l0 m/ sec 2 , then increase in the energy of the rod will be

The compressibility of water is 6 × 10 – 10 N – 1 m 2 . If one litre is subjected to a pressure of 4 x 10 7 N m – 2 , the decrease in its volume is

Two parallel and opposite forces each 5000 N are applied tangentially to the upper and lower faces of a cubical metal block of side 25 cm. The angle of shear is (The shear modulus of the metal is 80 GPa)

A 5 metre long wire is fixed to the ceiling. A weight of 10 kg is hung at the lower end and is I metre above the floor. The wire was elongated by I mm. The energy stored in the wire due to stretching is

A 2 m long rod of radius I cm which is fixed from one end is given a twist of 0.8 radians. The shear strain developed will be

The lower surface of a cube is fixed. On its upper surface, force is applied at an angle of 30° from its surface. The change will be of the type

A cube of aluminium of sides 0.1 m is subjected to a shearing force of 100 N. The top face of the cube is displaced through 0.02 cm with respect to the bottom face. The shearing strain would be

The compressibility of a material is

When a pressure of 100 atmosphere is applied on a spherical ball, then its volume reduces to 0.01%. The bulk modulus of the material of the rubber in dyne/ cm 2 is

A ball falling in a lake of depth 200 m shows 0.1% decrease in its volume at the bottom. What is the bulk modulus of the material of the ball?

What increase in pressure is required to decrease the volume of 200 litre of water by 0.004 percent? Given bulk modulus of water is 2100 MPa.

Two wires of diameter 0.25 cm, one made of steel and other made of brass are loaded as shown in figure. The unloaded length of the steel wire is 1.5 m and that of brass is 1.0 m. Young’s modulus of steel is 2.0 x 10 11 Pa and that of brass is 1.0 x 10 11 Pa. The ratio of elongations of steel and brass wires. ( ∆ l steel ∆ l brass = ? )

The two wires shown in figure are made of the same material which has a breaking stress of 8 x 10 8 N / m 2 . The area of the cross-section of the upper wire is 0.006 cm 2 and that of the lower wire is 0.003 cm 2 . The mass m 1 = 10 kg , m 2 = 20 kg and the hanger is light. The maximum load that can be put on the hanger without breaking a wire is

The product of Young’s modulus of the material of the wire with its cross-sectional area is equal to its length. Find the parameters representing x and y-axes of the curve as shown:

A steel ring of radius r and cross-section area ‘A’ is fitted on to a wooden disc of radius R (R > r). If Young’s modulus be E, then the force with which the steel ring is expanded is

A substance breaks down under a stress of 10 5 Pa. If the density of the substance is 2 x 10 3 kg/ m 3 , find the minimum length of the wire made of this substance which will break under its own weight (g = 10 m / s 2 )

The stress-strain curves for brass, steel and rubber are shown in the figure. The lines A, B and, C are for

Figure shows the strain-stress curve for a given material. The Young’s modulus of the material is G

The strain-stress curves of three wires of different materials are shown in the figure. P, Q and R are the elastic limits of the wires. The figure shows that

Two wires A and B are of same materials. Their lengths are in the ratio I : 2 and diameters are in the ratio 2 : I when stretched by force F A and F B respectively they get equal increase in their lengths. Then the ratio F A F B should be

There are two wires of same material and same length while the diameter of second wire is 2 times the diameter of first wire, then ratio of extension produced in the wires by applying same load will be

A steel rod of length 1 m and radius 10 mm is stretched by a force 100 kN along its length. The percentage strain produced in the rod is Y steel = 2 × 10 11 Nm – 2

A steel rod of length 1 m and radius 10 mm is stretched by a force 100 kN along its length. The stress produced in the rod is Y Steel = 2 × 10 11 Nm − 2

A steel rod is pulled by a force which increases gradually from zero to F and elongation produced in the rod is found to be x. If the some rod is pulled by a constant force 4F, the elongation produced in the rod will be

A rod AB of uniform cross-sectional area is subjected to an axial tensile force F. If the maximum normal force induced in the rod is 8 KN/cm 2 , the maximum shear stress induced in the rod will be

The maximum angular velocity with which a thin rod can be rotated about an axis passing through its centre c and perpendicular to the length without causing rupture is ‘ ω ‘ . Then what is the safe angular velocity with which the same rod can be rotated about an axis passing through one end and perpendicular to its length?

A cylindrical rod is subjected to axial tensile force as shown in figure. If Poisson’s ratio of the material of the rod is 0.25 and longitudinal strain produced in the rod is 0.05, then percentage change in the volume of the rod is

A rad AB of uniform cross sectional area is under the action of an axial tensile force as shown in figure. Poisson’s ratio of the material of the rod is 0.4 and percentage increase in the volume of the rod is 2%. Then longitudinal strain produced in the rod is

The composite rod ABC is acted upon by a tensile force F as shown in figure. Radius of AB is r and that of BC is 2r. If the total elastic potential energy stored in the rod is 100 Joule, the energy stored in the rod AB is Y AB = Y and Y BC = 2 Y

A block B of mass 20 Kg is suspended by a metallic rod of length 2 m, mass 10 Kg cross sectional area 4 mm 2 and young’s modulus 2 × 10 10 N / m 2 . Then elongation produced in the rod is

A metallic cube is acted upon by a tensile force F acting normally on each of six faces as shown in figure. If Poisson’s ratio of metal is 0.2 and longitudinal strain produced in the cube is 0.01, then percentage change produced in the volume is

When a metallic rod AB of length l = 1m, cross-sectional area 1 cm 2 and young’s modulus Y = 2 × 10 10 N / m 2 is heated through a temperature of 20 o C, its thermal expansion is found to be 2 mm. Now the rod is cooled to its original temperature and placed between two walls as shown in the figure. The walls are not perfectly rigid. Now when the rod is heated through a temperature of 20 o C, the walls get deformed at the points of contact with the rod and increase in length of the rod is found to be 1 mm. Then compressive force induced in the rod is

A block of mass 50 kgk is suspended by two strings 1 and 2 as shown in figure. The strings are of same length. Cross sectional area and young’s modulus of the string 1 are A and Y and those of string 2 are 2A and 2Y respectively. If the block always remains horizontal, tension induced in string 1 is

If there is no change in the volume of wire on stretching, then poisson’s ratio for material of wire is :

A rod is elongated by applying a force along its length such that Bulk strain of the rod is zero. Poisson’s ratio of the rod is

Two wires of the same material and length, having diameters in the ratio 2 : 1, are stretched by the same force. The potential energy per unit volume stored in the two wires will be in the ratio:

A copper wire and a steel wire of the same diameter and length are connected end to end and a force is applied, which stretches their combined length by 1 cm. The two wires will have

A 5 m long aluminum wire Y = 7 × 10 10 N / m 2 of diameter 3 mm supports a 40 kg mass. In order to have the same elongation in a copper wire Y = 12 × 10 10 N / m 2 of the same length under the same weight, the diameter should now be (in mm).

A pan with set of weights is attached with a light spring. When disturbed, the mass-spring system oscillates with a time period of 0.6 s. When some additional weights are added, then time period is 0.7s. The extension caused by the additional weights is approximately given by

The area of cross section of a steel wire Y = 2 .0 × 10 11 N / m 2 is 0.1 cm 2 . The force required to double its length will be

A ball falling in a lake of depth 200 m shows 0.1 % decrease in its volume at the bottom. What is the bulk modulus of the material of the ball?

A brass rod of cross-sectional area 1 cm 2 and length 0.2 m is compressed lengthwise by a weight of 5 kg. If Yourg’s modulus of elasticity of brass is 1 × 10 11 N / m 2 and g = 10 m s – 2 then increase in the energy of the rod will be

A 5-metre long wire is fixed to the ceiling. A weight of 10 kg is hung at the lower end and is 1 metre above the floor. The wire was elongated by 1 mm. The energy stored in the wire due to stretching is

The diagram below shows a force-extension graph for a rubber band. Consider the following statements: i. It will be easier to compress this rubber than expand it. ii. Rubber does not return to its original length after it is stretched. iii. The rubber band will get heated if it is stretched and released. Which of these can be deduced from the graph?

The load-versus-elongation graph for four wires of the same material is shown in the figure. The thickest wire is represented by the line

The mass and length of a wire are M and Z, respectively. The density of the material of the wire is d. On applying the force F on the wire, the increase in length is l. Then the Young’s modulus of the material of the wire will be

To break a wire of one meter length, minimum 40 kg-wt is required. Then the wire of the same material of double radius and 6 m length will require breaking weight

The potential energy U between two molecules as a function of the distance X between them has been shown in the figure. The two molecules are

Two exactly similar wires of steel and copper are stretched by equal forces. If the difference in their elongations is 0.5 cm, the elongation (I) of each wire is Y s ( steel ) = 2 .0 × 10 11 N / m 2 Y c ( copper ) = 1 .2 × 10 11 N / m 2

A rectangular block of size 10 cm x 8 cm x 5 cm is kept in three different positions P, Q and R in turn as shown in the figure. In each case, the shaded area is rigidly fixed and a definite force F is applied tangentially to the opposite face to deform the block. The displacement of the upper face will be

The ratio of diameters of two wires of same material is n:1. The length of each wire is 4 m. On applying the same load, the increases in the length of the thin wire will be (n > l)

A nylon rope 2 cm in diameter has a breaking strength of 1.5 x 10 5 N. The breaking strength of a similar rope 1 cm in diameter is

The breaking stress for a substance is 10 6 N/ m 2 . what length of the wire of this substance should be suspended vertically so that the wire breaks under its own weight? (Given : density of material of the wire = 4 x 10 3 kg/m 3 and g = 10 ms -2 )

The dimensions of four wires of the same material are given below. In which wire the increase in the length will be maximum?

Two wires of the same material and length are stretched by the same force. Their masses are in the ratio 3:2. Their elongations are in the ratio

When a weight of 5 kg is suspended from a copper wire of length 30 m and diameter 0.5 mm, the length of the wire increases by 2.4 cm. If the diameter is doubled, the extension produced is

The length of a wire is increased by 1 mm on the application of a given load. In a wire of the same material, but of length and radius twice that of the first, on application of the same load, extension is

Young’s modulus of rubber is 10 4 N/m 2 and area of cross section is 2 cm 2 . If force of 2 x 10 5 dyn is applied along its length , length increases by 1m, then its initial length l becomes

When a certain weight is suspended from a long uniform wire, its length increases by 1 cm. If the same weight is suspended from another wire of the same material and length but having a diameter half of the first one, the increases in length will be

Two wires of the same material have lengths in the ratio 1:2 and their radii are in the ratio 1 : 2 . If they are stretched by applying equal forces, the increase in their lengths will be in the ratio

Two identical wires of iron and copper with their Young’s modulus in the ratio 3:1 are suspended at same level. They are to be loaded so as to have the same extension and hence level. Ratio of the weight is

A wire is stretched 1 mm by a force of 1 kN How far would a wire of the same material and length but of four times that diameter be stretched by the same force?

A copper bar of length L and area of cross section A is placed in a chamber at atmospheric pressure. If the chamber is evacuated, the percentage change in its volume will be (compressibility of copper is 8 × 10 − 12 m 2 / N and 1 atm = 10 5 N/m)

The diagram shows stress vs. strain curve for the materials A and B. From the curves we infer that

What amount of work is done in increasing the length of a wire through unity?

When the load on a wire is slowly increased from 3 to 5 kg wt, the elongation increases from 0.61 to 1.02 mm. The work done during the extension of wire is

Two wires of the same material and length but diameters in the ratio 1:2 are stretched by the same force. The potential energy per unit volume for the two wires when stretched will be in the ratio

If the potential energy of a spring is V on stretching it by 2 cm, then its potential energy when it is stretched by 10 cm will be

If the work done by stretching a wire by 1 mm is 2 J, the work necessary for stretching another wire of the same material but with double the radius of cross section and half the length by 1 mm is

Two wires of the same diameter and of the same material have the length l and 2l. lf the force F is applied on each, the ratio of the work done in the two wires will be

The force (F)-extension ( Δl ) , graph shows that the strain energy stored in the material under test, for an extension of 4 mm, is greater than which of the following values?

The length of a rod is 20 cm and area of cross-section 2 cm 2 . The Young’s modulus of the material of wire is 1.4 × 10 11 N / m 2 . If the rod is compressed by 5 kg-wt along its length, then increase in the energy of the rod in joules will be

When a force is applied on a wire of uniform crosssectional area 3 × 10 − 6 m 2 and length 4 m, the increase in length is 1 mm. Energy stored in it will be Y = 2 × 10 11 N / m 2

A wire of cross section A is stretched horizontally between two clamps located 2l m apart. A weight W kg is suspended from the mid-point of the wire. If the mid-point sags vertically through a distance x < 1 the strain produced is

When the tension in a metal wire is T 1 , its length is l 1 . When the tension is T 2 , its length is l 2 .The natural length of wire is

A ball falling in a lake of depth 200 m shows a decrease of 0.1% in its volume at the bottom. The bulk modulus of the elasticity of the material of the ball is take g = 10 ms − 12

Two bars A and B of circular cross section, same volume and made of the same material, are subjected to tension. If the diameter of A is half that of B and if the force applied to both the rod is the same and it is in the elastic limit, the ratio of extension of A to that of B will be

A uniform cylindrical wire is subjected to a longitudinal tensile stress of 5 × 10 7 N / m 2 . Young’s modulus of the material of the wire is 2 × 10 11 N / m 2 . The volume change in the wire is 0.02%.The fractional change in the radius is

Maximum excess pressure inside a thin-walled steel tube of radius r and thickness Δr ( << r ) , so that the tube, would not rupture would be (breaking stress of steel is σ max )

A wire can sustain the weight of 20 kg before breaking. If the wire is cut into two equal parts, each part can sustain a weight of

A mass m is hanging from a wire of cross-sectional area A and length L. Y is Young’s modulus of wire. An external force F is applied on the wire which is then slowly further pulled down by ∆ x from its equilibrium position. Find the work done by the force F the wire exerts on the mass.

Wires A and B are connected with blocks P and Q, as shown. The ratio of lengths, radii and Young’s modulus of wires A and B are r, 2r and 3r respectively (r is a constant). Find the mass of block P it ratio of increase in their corresponding lengths is 1 6 r 2 . The mass of the block Q is 3M.

Two parallel and opposite forces, each of magnitude 4000 N, are applied tangentially to the upper and lower faces of a cubical metal block 25 cm on a side. Find the displacement of the upper surface relative to the lower surface (in x 10 -5 cm ). The shear modulus for the metal is 80 Gpa.

A hydraulic press contains 0.25 m 3 (250 L) of oil. Find the decrease in volume of the oil (in %) when it is subjected to a pressure increase Δp = 1 .6 × 10 7 . The bulk modulus of the oil is B = 5 .0 × 10 9 Pa.

A 0.05 m cube has its upper face displaced by 0.2 cm by a tangential force of 8 N. Calculate the modulus of rigidity in × 10 4 Nm − 2 of the material of the cube.

Bulk modulus for rubber is 9.8 × 10 8 Nm − 2 . To what depth (in m) should a rubber ball be taken in a lake so that its volume is decreased by 0.1%?

The average depth of Indian ocean is about 3000 m. Find the percentage of compression ΔV V of water of the bottom of the ocean. Given, bulk modulus of water is 2 .2 × 10 9 Nm − 2 and density of water = 1000 kgm − 3 .

A solid sphere of radius R made of a material of bulk modulus B is surrounded by a liquid in a cylindrical container. A massless piston of area A (the area of container is also A) floats on the surface of the liquid. When a mass m is placed on the piston to compress the liquid, find the fractional change in radius of the sphere. (Given, Mg AB = 0.3)

Find the elastic potential energy per unit volume of water in × 10 3 Jm − 3 at a depth of 1 km. Given, compressibility of water = 5 × 10 10 SI units and density of water = 1000 kgm − 3 .

Figure shows a graph of the extension (A) of a wire of length 1 m suspended from the top of a roof at one end and with a load W connected to the other end. If the cross-sectional area of the wire is 10 – 6 m 2 , the Young’s modulus of the material of the wire is x × 10 11 N / m 2 . The value of x is

If a rubber cube is taken 50 m deep in a lake, its volume reduces by 0.5%. The bulk modulus of rubber is nearly.

A uniform rod is rotating about one of its end with a constant angular velocity ω in gravity free space. The radial strain produced in two halves is k > 1 . Then find the value of 20 k 11 .

The Young’s modulus of a wire of length L and radius r is Y N/m 2 . If the length and radius are reduced to L/2 and r/2, then its Young’s modulus will be

A beam of metal supported at the two ends is loaded at the centre. The depression at the centre is proportional to

When a certain weight is suspended from a long uniform wire, its length increases by one cm. If the same weight is suspended from another wire of the same material and length but having a diameter half of the first one then the increase in length will be

Hook’s law defines

A wire is loaded by 6 kg at its one end, the increase in length is 12 mm. If the radius of the wire is doubled and all other magnitudes are unchanged, then increase in length will be

The area of cross-section of a wire of length 1.1 metre is 1 mm 2 . It is loaded with 1 kg. If Young’s modulus of copper is 1 .1 × 10 11 N / m 2 , then the increase in length will be (If g = 10 m / s 2 )

On increasing the length by 0.5 mm in a steel wire of length 2 m and area of cross-section 2 mm 2 , the force required is [Y for steel = 2 .2 × 10 11 N / m 2 ] ]

If Young’s modulus of iron is 2 × 10 11 N / m 2 and the interatomic spacing between two molecules is 3 × 10 − 10 metre, the interatomic force constant is

In CGS system, the Young’s modulus of a steel wire is 2 × 10 12 dyne / cm 2 . To double the length of a wire of unit cross-sectional area, the force required is

The material which practically does not show elastic after effect is

If the temperature increases, the modulus of elasticity

A force F is needed to break a copper wire having radius R. The force needed to break a copper wire of radius 2R will be

The relationship between Young’s modulus Y, Bulk modulus K and modulus of rigidity η is

The diameter of a brass rod is 4 mm and Young’s modulus of brass is 9 × 10 10 N / m 2 . The force required to stretch by 0.1% of its length is

If x longitudinal strain is produced in a wire of Young’s modulus Y, then energy stored in the material of the wire per unit volume is

In a wire of length L, the increase in its length is l. If the length is reduced to half, the increase in its length will be

The Young’s modulus of a rubber string 8 cm long and density 1 .5 kg / m 3 is 5 × 10 8 N / m 2 , is suspended on the ceiling in a room. The increase in length due to its own weight will be

If the length of a wire is reduced to half, then it can hold the ……… load

The spring balance does not read properly after its long use, because

A and B are two wires. The radius of A is twice that of B. They are stretched by the same load. Then the stress on B is

To double the length of a iron wire having 0.5 cm 2 area of cross-section, the required force will be ( Y = 10 12 dyne / cm 2 )

Two wires of equal lengths are made of the same material. Wire A has a diameter that is twice as that of wire B. If identical weights are suspended from the ends of these wires, the increase in length is

Two wires of copper having the length in the ratio 4 : 1 and their radii ratio as 1 : 4 are stretched by the same force. The ratio of longitudinal strain in the two will be

The ratio of diameters of two wires of same material is n : 1. The length of wires are 4 m each. On applying the same load, the increase in length of thin wire will be

Longitudinal stress of 1 kg / mm 2 is applied on a wire. The percentage increase in length is ( Y = 10 11 N / m 2 )

If a load of 9 kg is suspended on a wire, the increase in length is 4.5 mm. The force constant of the wire is

The interatomic distance for a metal is 3 × 10 − 10 m . If the interatomic force constant is 3 .6 × 10 − 9 N / Å , then the Young’s modulus in N / m 2 will be

A steel wire is stretched with a definite load. If the Young’s modulus of the wire is Y. For decreasing the value of Y

The force constant of a wire does not depend on

Two identical wires of rubber and iron are stretched by the same weight, then the number of atoms in the iron wire will be

After effects of elasticity are maximum for

In suspended type moving coil galvanometer, quartz suspension is used because

A force of 200 N is applied at one end of a wire of length 2 m and having area of cross-section 10 − 2 cm 2 . The other end of the wire is rigidly fixed. If coefficient of linear expansion of the wire α = 8 × 10 − 6 / ° C and Young’s modulus Y = 2 .2 × 10 11 N / m 2 and its temperature is increased by 5°C, then the increase in the tension of the wire will be

When compared with solids and liquids, the gases have

The length of a wire is 1.0 m and the area of cross-section is 1 .0 × 10 − 2 cm 2 . If the work done for increase in length by 0.2 cm is 0.4 joule, then Young’s modulus of the material of the wire is

The quality of the material which opposes the change in shape, volume or length is called

For silver, Young’s modulus is 7 .25 × 10 10 N / m 2 and Bulk modulus is 11 × 10 10 N / m 2 . Its Poisson’s ratio will be

The longitudinal strain is only possible in

Young’s modulus of rubber is 10 4 N / m 2 and area of cross-section is 2 cm 2 . If force of 2 × 10 5 dynes is applied along its length, then its initial length l becomes

The elastic limit for a gas

Liquids have no Poisson’s ratio, because

If Young’s modulus for a material is zero, then the state of material should be

The force required to stretch a steel wire of 1 cm 2 cross-section to 1.1 times its length would be ( Y = 2 × 10 11 Nm − 2 )

Which of the following statements is correct

The adjacent graph shows the extension ( Δ l ) of a wire of length 1 m suspended from the top of a roof at one end and with a load w connected to the other end. If the cross-sectional area of the wire is 10 – 6 m 2 , calculate from the graph the Young’s modulus of the material of the wire.

In Searle’s experiment, which is used to find Young’s modulus of elasticity, the diameter of experimental wire is D = 0 . 05 cm (measured by a scale of least count 0 . 001 cm ) and length is L = 110 cm (measured by a scale of least count 0 . 1 cm ) . A weight of 50 N causes an extension of l = 0 . 125 cm (measured by a micrometer of least count 0 . 001 cm ). Find maximum possible error in the value of Young’s modulus. Screw gauge and meter scale are free from error.

A student performs an experiment to determine Young’s modulus of a wire, exactly 2 m long by Searle’s method. In a particular reading, the student measures the extension in the length of the wire to be 0.8 mm with an uncertainty of ± 0 . 05 mm at a load of 1 . 0 kg (exact). The student also measures the diameter of the wire to be 0 . 4 mm with an uncertainty of ± 0 . 01 mm . Take g = 9 . 8 m / s 2 (exact). Find Young’s modulus of elasticity with limits of error.

Which of the following is wrong regarding Searle’s apparatus method in finding Young’s modulus of a given wire?

A metal bar of length L, area of cross-section A, Young’s modulus Y and coefficient of linear expansion α , is clamped between two stout pillars. Now it is heated through t° C. The force exerted by the bar is

A spherical ball contracts in volume by 00.01% when subjected to a normal uniform pressure of 100 atmospheres. The bulk modulus of its material in dyne/cm 2 is

Two wires A and B are of the same material. Their lengths are in the ratio 1 : 2 and the diameters are in the ratio 2 : 1. If they are pulled by the same force, their increase in length will be in the ratio

The bulk modulus of rubber is 9.1 x 10 8 N/m 2 . To what depth a rubber ball be taken in a lake so that its volume is decreased by 0.1%?

An aluminum rod, Young’s modulus 7.0×10 9 newton/metre 2 has a breaking strain of 0.2%. The minimum cross-sectional area of the rod in m 2 in order to support a load of 10 4 newton is

In a wire stretched by hanging a weight from its end, the elastic potential energy per unit volume in terms of the longitudinal strain σ and modulus of elasticity Y is

When an elastic material with Young’s modulus Y is subjected to a stretching stress s, the elastic energy stored per unit volume of the material

A long string is stretched by 2 cm and the potential energy V. If the spring is stretched by 10 cm, its potential energy will be

A uniform heavy rod of weight W, cross-sectional area A and initial length I is suspended from a rigid support. f is the Young’s modulus of the material of the wire. If no Iateral contraction is taken into account, the elongation of the rod will be

A wire suspended vertically from one of its ends is stretched by attaching a weight of 200 N to the lower end. The weight stretches the wire by 1 mm. Then, the elastic energy stored in the wire is

A uniform rod of length L and density p is being pulled along a smooth floor with a horizontal acceleration α (see fig). The magnitude of the stress at the transverse cross-section trough the mid-point of the rod is

A thick rope of density p and length f, is hung from a rigid support. The Young’s modulus of the material of rope is Y. The increase in length of the rope due to its own weight is

The bulk modulus of rubber is 9 x 10 8 N/m 2 . To what depth below the surface of sea should the rubber ball be taken as to decrease its volume by 0.1%?

There is no change in the volume of a wire due to change in its length on stretching. The Poisson’s ratio of the material of the wire is

A spherical ball contracts in volume by 0.02% when subjected to a pressure of 100 atmosphere. Assuming one atmosphere = 10 5 Nm – 2 , the bulk modulus of the material of the ball is

A material has Poisson’s ratio 0.50. If a uniform rod of it suffers a longitudinal strain of 2 x10 -3 , then the percentage change in volume is

A solid sphere of radius R made of material of bulk modulus K is surrounded by a liquid of cylindrical container. A massless piston of area A floats on the surface of the liquid when a mass M is placed on the piston to compress the liquid, the fractional change in the radius of the sphere is

The normal density of gold is p and its bulk modulus is K The increase in density of a lump of gold when a pressure P applied uniformly on all side is

One end of a uniform wire of length L and of weight W is attached rigidly to a point in the roof and a weight W, is suspended from its lower end. If S is the area of cross-section of the wire, the stress in the wire at height (3 L/ 4) from its lower end is

A wire fixed at the upper end stretches by length l by appling a force F. The work done in stretching is

The load versus elongation graph for four wires of same material is shown in fig. [4). The thinnest wire is represented by the line

Fig shows the extension ∆ l of a wire of length one metre suspended from the top of a roof at one end and with a load W connected to the other end. If the cross-sectional area of the wire is 10 -6 m 2 , the Young s modulus of the material of the wire will be

A metal rod (Young’s modulus Y) has a length I and of cross-section A. The work done in stretching the rod by an amount ∆ L is

A wire of radius r stretched without tension along a straight line is lightly fixed at A and B as shown in fig. What is the tension in the wire when it is pulled into the shape A C B ? Assume Young’s modulus of the material of the wire to be Y and d < l

Two cylinders A and I [Fig. (2)] of the same material have same length, their radii being in the ratio 1 : 2 ,respectively. The upper end of A is rigidly fixed. The lower end of B is twisted through an angle 0. The angle of twist of the cylinder A is

Figure shows the strain-stress curve for a given material. The Young’s modulus of the material is

Two rods A and B of equal free lengths hang vertically from ceiling 60 cm apart and at bottom attached to a light horizontal bar. The bar remain in horizontal position when carry a load of 5000 kg at a distance 20 cm from rod A. If the stress in rod B is 50 N/mm 2 , find the stress in A (in N/mm 2 ) up to two decimal places. Take Young’s moduli are Y B = 9 × 10 10 N / m 2 , Y A = 2 × 10 11 N / m 2 and g = 10 m / s 2 .

Two opposite forces F 1 = 120 N and F 2 = 80 N act on an elastic plank of modulus of elasticity Y = 2 × 10 11 N / m 2 and length l = 1 m placed over a smooth horizontal surface. If the cross-sectional area of the plank is S = 0.5 m 2 , the change in length of the plank is nm.

A metal wire of length L 1 and area of cross-section A is attached to a rigid support. Another metal wire of length L 2 and of the same cross-sectional area is attached to the free end of the first wire. A body of mass M is then suspended from the free end of the second wire. If Y 1 and Y 2 are the Young’s moduli of the wires respectively, the effective force constant of the system of two wires is

A copper wire of length 3 m and area of cross-section 1 mm 2 , passes through an arrangement of two frictionless pulleys, P 1 and P 2 . One end of the wire is rigidly clamped and a mass of 1 kg is hanged from the other end. If the Young’s modulus for copper is 10 x 10 10 N/m 2 , then the elongation (in mm) in the wire is . Take g = 10ms -2 .

A bar of length l, breadth b and depth d is supported at its ends and is loaded at the centre by a load W. If Y is the Young’s modulus of the material of the bar, then the depression δ at the centre is

Two rods A and B of the same material and length have radii r 1 and r 2 respectively. When they are rigidly fixed at one end and twisted by the same torque applied at the other end, the ratio the angle of twist at the end of A the angle of twist at the end of B equals to

When a block of mass M is suspended by a long wire of length L, the length of the wire becomes (L + l ). The elastic potential energy stored in the extended wire is [NEET 2019]

A solid sphere of radius R, made up of a material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area A floats on the surface of the liquid. When a mass M is placed on the piston to compress the liquid, the fractional change in the radius of the sphere is

A 5 m long wire is fixed to the ceiling. A weight of 10 kg is hang at the lower end and is 1m above the floor. The wire was elongated by 1mm. The energy stored in the wire due to stretching is

An elastic material with Young’s modulus Y is subjected to a tensile stress S, elastic energy stored per unit volume of the material is

Two wires of copper having the length in the ratio 4 : 1 and their radii ratio as 1 : 4 are stretched by the same force. The ratio of longitudinal strain in the two will be

Two wires of same diameter of the same material having the length l and 2 l . If the force F is applied on each, the ratio of the work done in the two wires will be

The increase in length on stretching a wire is 0.05%. If its Poisson’s ratio is 0.4, then its diameter

For steel Y = 2 × 10 11 Nm − 2 then the force required to double the length of a steel wire of area 1 cm 2 is

In the given figure, if the dimensions of the wires are the same and materials are different, Young’s modulus is more for

A cable that can support a load w is cut into two equal parts. The maximum load that can be supported by either part is

A uniform steel bar of cross-sectional area A and length L is suspended, so that it hangs vertically. The stress at the middle point of the bar is ( ρ is the density of steel)

The load versus elongation graph for four wires of the same material is shown in the figure. The thickest wire is represented by the line

If compressibility of a material is 4 X 10 -5 per atm, pressure is 100 atm and volume is 100 cm 3 , then find the value of Δ V . [JIPMER 2018]

A stress of 10 6 Nm -2 is required for breaking a material. If the density of the material is 3 x 10 3 kgm -3 , then what should be the length of the wire made of this material, so that it breaks under its own weight?

A thick rope of rubber of length 8 m and density 1.5 X 10 3 kgm -3 has Young’s modulus 5 x 10 6 Nm -2 . When hung from ceiling of a room, the increase in length due to its own weight is

Which of the following statement{s) is/are correct? I. Incompressible liquids have finite value of bulk modulus of elasticity. II. Compressibility is inverse of bulk modulus of elasticity.

Theoretically, the value of Poisson’s ratio σ lies between

The diagram shows a force-extension graph for a rubber band. Consider the following statements. I. It will be easier to compress this rubber than expand it. II. Rubber does not return to its original length after it is stretched. III. The rubber band will get heated, if it is stretched and released. Which of the following statement{s) is/are correct regarding the graph?

With regard to dependence of quantities given in Columns I and II, match the following columns and choose the correct option from the codes given below. Column I (A) Young’s modulus of a substance (B) Bulk modulus of a substance (C) Modulus of rigidity of a substance (D) Volume of a substance Column II (p) depends on temperature (q) depends on length (r) depends on area of cross-section (s) depends on the nature of material

The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?

Longitudinal stress of 1 N mm -2 is applied on a wire. The percentage increase in length is (Take, Y = 10 11 Nm -2 )

The temperature of a wire of length 1 m and area of cross-section 1 cm 2 is increased from 0 0 C to 100 0 C. If the rod is not allowed to increase in length, the force required will be ( α = 10 -5 / 0 C and Y = 10 11 Nm -2 )

If Poisson’s ratio cr for a material is 1 2 , then the material is [BCECE (Mains) 2012]

A cable is replaced by another one of the same length and material but of twice the diameter. The maximum load that the new wire can support without exceeding the elastic limit, as compared to the load that the original wire could support, is

If the Young’s modulus of the material is 3 times its modulus of rigidity, then its volume elasticity will be

A steel wire of cross-sectional area 3 x 10 -6 m 2 can withstand a maximum strain of 10 -3 , Young’s modulus of steel is 2 X 10 11 Nm -2 . The maximum mass this wire can hold is

The temperature of a wire is doubled. The Young’s modulus of elasticity

An elevator cable is to have a maximum stress of 7 x 107 Nm -2 to allow for appropriate safety factors. Its maximum upward acceleration is 1.5 ms -2 . If the cable has to support the total weight of 2000 kg of a loaded elevator, the area of cross-section of the cable should be

A metal block is experiencing an atmospheric pressure of 10 5 Nm -2 . When the same block is placed in a vacuum chamber, the fractional change in its volume, is (the bulk modulus of metal is (1.25 X 10 11 Nm -2 )

A copper wire (Y = 10 11 Nm -2 ) of length 8 m and a steel wire (Y = 2 X 10 11 Nm -2 ) of length 4 m, each of 0.5 cm 2 cross-section are fastened end-to-end and stretched with a tension of 500 N. Choose the correct statement.

A steel wire of length I a nd cross-section area A is stretched by 1 cm under a given load. When the same load is applied to another steel wire of double its length and half of its cross-section area, the amount of stretching is

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by ∆ l on applying a force F, how much force is needed to stretch the second wire by the same amount?

For most of the material, Young’s modulus ( Y ) and rigidity modulus ( G ) are related as

Two wires of same material having radius in ratio 2 : 1 and lengths in ratio 1 : 2. If same force is applied on them, then ratio of their change in length will be

The elastic potential energy of a stretched wire is given by

The bulk modulus of a spherical object is B . If it is subjected to uniform pressure p , the fractional decrease in radius is [NEET 2017]

A mild steel wire of length 2 L and cross-sectional area A is stretched, well within elastic limit, horizontally between two pillars (figure ). A mass m is suspended from the mid-point of the wire. Strain in the wire is [NCERT Exemplar]

The maximum load, a wire can withstand without breaking, when its length is reduced to half of its original length, will [NCERT Exemplar]

The Young’s modulus of a wire is Y, if the energy per unit volume is E, then the strain will be

Young’s modulus of the material of a wire of length L and radius r is Y Nm -2 . If the length is reduced to L 2 and radius to r 2 , the Young’s modulus will be

The length of an elastic string is a metre when the tension is 4 N and b metre when the tension is 5 N. The length, (in metre), when the tension is 9 N, is

Two block of masses of 1 kg and 2 kg are connected by a metal wire going over a smooth pulley. The breaking stress of metal is 40 3 π × 10 6 Nm − 2 What should be the minimum radius of wire used, if it should not break? (Take, g = 10 ms -2 ). [Manipal 2012]

The density of a metal at normal pressure is ρ . Its density when it is subjected to an excess pressure P is ρ ‘. If B is the bulk modulus of the metal, then the ratio ρ ‘/ ρ is

If to break a wire of 1 m length, minimum 40 kg-wt is required, then to break a wire of same material 6 m in length and double in radius, the breaking weight required will be

A stress of 6 X 10 6 N m – 2 required for breaking a material. The density ρ of the material is 3 X 10 3 kg m – 3 . If the wire is to break under its own weight, the length of the wire made of that material should be (Take, g = 10 m s – 2 )

In designing, a beam for its use to support a load. The depression at centre is proportional to (where, Y is Young’s modulus).

A rubber cord L metre long and having A m 2 area of cross-section is suspended vertically. If the wire extends 1 m under its own weight, then change in length ( I ) is (Take, density of rubber = D kgm -3 and Young’s modulus of rubber = E Nm -2 ).

Two wires of same length and same material but of radii r and 2 r are stretched by forces F and f respectively to produce equal elongation. The ratio F to f is

A steel wire of length 2 m and 1.2 × 10 − 7 m 2 in cross-sectional area is stretched by a force of 36 N. Calculate the work done in × 10 − 2 J stretching the wire Y = 1 .8 × 10 11 N / m 2 .

Two wires of the same material have lengths in the ratio 1 : 2 and radii are in the ratio 1 : √2. If they are stretched by applying equal forces, the increase in their lengths will be in the ratio

For steel Y = 2 × 10 11 Nm − 2 , then the force required to double the length of a steel wire of area 1 cm 2 is

Two wires of copper having the length in the ratio 4 : 1 and their radii ratio as 1 : 4 are stretched by the same force. The ratio of longitudinal strain in the two will be

A metal block is experiencing an atmospheric pressure of 10 5 Nm − 2 .When the same block is placed in a vacuum chamber, the fractional change in its volume, is (the bulk modulus of metal is 1 .25 × 10 11 Nm − 2 )

The Young’s modulus of a wire is numerically equal to the stress which will

A rubber cord 10 m long is suspended vertically. How much does it stretch under its own weight (Density of rubber is 1500 kg / m 3 , Y = 5 × 10 8 N / m 2 , g = 10 m / s

When a force is applied on a wire of uniform cross-sectional area 3 × 10 − 6 m 2 and length 4m, the increase in length is 1 mm. Energy stored in it will be Y = 2 × 10 11 N / m 2

The length of an elastic string is ‘a’ meter when the tension is 4 N and ‘b’ meter when the tension is 5 N. The length, (in meter), when the tension is 9 N, is

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by Δl on applying a force F, how much force is needed to stretch the second wire by the same amount?

A rubber cord 10 m long is suspended vertically. How much does it stretch under its own weight (Density of rubber is 1500 kg/m 3 , Y = 5 × 10 8 N / m 2 , g = 10 m / s 2 .

If compressibility of a material is 4×10 -5 per atm. If pressure is 100 atm and volume is 100 cm 3 , then find the value of ΔV .

Which of the following statement{s) is/are correct? (I) Incompressible liquids have finite value of bulk modulus of elasticity. (II) Compressibility is inverse of bulk modulus of elasticity.

If Poisson’s ratio σ for a material is 1 2 , then the material is

A thin uniform metallic rod of length 0.5 m and radius 0.1 m with an angular velocity 400 rad s- 1 in a horizontal plane about a vertical axis passing through one of its ends. Elongation in the rod is (in m) [Given density of material of the rod is 10 4 kgm – 3 and Y = 2 × 10 11 Nm – 2 ]

A steel wire of length 4 m and diameter 5 mm is stretched by 5 kg-wt. The increase in its length, if the Young’s modulus of steel wire is 2 .4 × 10 12 dyne cm − 2 is

The strain-stress curves of three wires of different materials but of identical shape and size are shown in the figure. P, Q and R are the elastic limits of the wires, The figure shows that

A steel cable with a radius of 1.5 cm supports a chair lift at a ski area. If the maximum stress is not to exceed 10 8 N/m 2 , what is the maximum load the cable can support?

An elevator cable is to have a maximum stress of 7×10 7 Nm -2 to allow for appropriate safety factors. Its maximum upward acceleration is 15 ms -2 . If the cable has to support the total weight of 2000 kg of a loaded elevator, the area of cross-section of the cable should be

The temperature of a wire of length 1 m and area of cross-section 1 c m 2 is increased from 0 o to 100 o C. If the rod is not allowed to increase in length, the force required will be α = 10 − 5 / ∘ C and Y = 10 11 Nm − 2

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