Important Physics And Measurement Questions for CBSE Class 11th

The dimensional formula of EJ 2 M 5 G 2 where E, M, J and G denote energy, mass, angular momentum and gravitational constant is M a L b T c . Then the value of c is

A physical quantity is represented by X = M a L b T − c . If percentage errors in the measurements of M, L and T are α % , β % and γ % respectively, then total percentage error is

For the four sets of three measured physical quantities as given below. Which of the following options is correct? i A 1 = 24.36 , B 1 = 0.0724 , C 1 = 256.2 i i A 2 = 24.44 , B 2 = 16.082 , C 2 = 240.2 i i i A 3 = 25.2 , B 3 = 19.2812 , C 3 = 236.183 i v A 4 = 25 , B 4 = 236.191 , C 4 = 19.5

T he given diagram represents a screw gauge. The circular scale is divided into 50 divisions and the linear scale is divided into millimeters. If the screw advances by 1 mm when the circular scale make s 2 complete revolutions, the reading of the instrument in the figure is mm

From the equation tan ⁡ θ = r g v 2 , one can obtain the angle of banking θ for a cyclist taking a curve (the symbols have their usual meanings). Then, say, it is

The relative density of material of a body is found by weighing it first in air and then in water. If the weight in air is (5.00 ± 0.05) Newton and weight in water is (4.00 ± 0.05) Newton. Then the relative density along with the maximum permissible percentage error is

How many significant digits are present in the value of 6.5 − 6.32 ?

The mass of a body m moving with a velocity v is given by m = m 0 1 − v 2 c 2 where m 0 = rest mass, c = speed of light = 3 x 10 8 ms -1 . The value of m (in kg using significant figures) for m 0 = 10 kg , v = 3 × 10 7 ms − 1 is

During measurement of kinetic energy , the percentage error in measurement of mass of particle and momentum of particle are 2% and 3%, respectively. The percentage error in measurement of kinetic energy is .

In a new system of units a tower of height 76 m is represented by number 7.6, sugar sack of mass 100 kg is represented by number 10 and 1 hour time is represented by number 360. If a force is measured to be 4 N then the magnitude of force in this new system is units.

In an ancient civilization, the unit of length was half of meter, the unit of mass was double the kilogram and the unit of time was half of second. The ratio of joule and the new unit of energy is

Length of a year on a planet is the duration in which it completes one revolution around the sun. Assume path of the planet known as orbit to be circular with sun at the center. The length T of a year of a planet orbiting around the sun in circular orbit depends on universal gravitational constant G, mass m of the sun and radius r of the orbit. If T ∝ G a m b r c , the value of a + b + 2 c is

Young’s modulus of steel is 19 × 10 10 N / m 2 . Express it as x × 10 11 dyne / cm 2 . Here dyne is the CGS unit of force. The value of x is

The length of a wire is 2.17 cm and radius is 0.46 cm. The number of significant digits in the value of volume of wire is

The mass of a body is 20.000 g and its volume is 10.00 cm 3 . If the measured values are expressed to the correct significant figures, the maximum error in the value of density is

The percentage errors in the measurement of mass and speed are 2% and 3%, respectively. How much will be the maximum error in the estimation of KE obtained by measuring mass and speed?

The relative density of a material of a body is found by weighing it first in air and then in water. If the weight of the body in air is W 1 = 8.00 ± 0.05 N and the weight in water is W 2 = 6.00 ± 0.05 N , then the relative density ρ r = W 1 / W 1 − W 2 with the maximum permissible error is

If energy E, length L and, time T are taken as fundamental quantities. The dimensional formula of gravitational constant is

Each side of a cube is measured to be 7.203 m. The volume of the cube to appropriate significant figures is

Count total number of significant figures in the following measurement: 10.00 cm

You measure two quantities as A = 1.0 m ± 0.2 m , B = 0.2 m ± 0.2 m . We should report correct value for A B is

Consider a new system of units in which the unit of mass is α kg, unit of length is β m and that of time is γ s. The value of calorie in the new system is calculated to be 4 . 18 α – x β – y γ z . Find the values of z.

The mean length of an object is 5 cm. Which of the following measurements is most accurate?

Percentage error in the measurement of mass and speed are 2 % a n d 3 % , respectively. The error in the measurement of kinetic energy obtained by measuring mass and speed will be

Three measurements are, a = 25 . 6 , b = 21 . 1 a n d c = 2 . 43 . Find the value a – b – c to correct significant figures.

The length, breadth and thickness of a block are given by l = 12 cm , b = 6 cm and t = 2 . 45 cm . The volume of the block according to the idea of significant figures should be

A physical quantity \rho is related to four variables α , β , γ and η as ρ = α 3 β 2 η γ The percentage errors of measurements in α , β , γ and η are 1 % , 3 % , 4 % a n d 2 % , respectively. Find the percentage error in ρ .

The radius of a cylindrical wire is measured by screw gauge is 1 . 25 mm . The length of wire is 25 . 0 cm and the mass of wire is 12 g . The density of wire is

Find the dimensional formula of Work or Energy.

Simplify and round to the appropriate number of significant digits: 0 . 00435 × 4 . 6

If we measure a length I = 6 . 24 cm with the help of a vernier callipers, then how many significant figures are there in the measured length?

Find the percentage error in specific resistance given by ρ = π r 2 R l , where r is the radius having value ( 0 . 2 ± 0 . 02 ) cm , R is the resistance of ( 60 ± 2 ) o h m and l is the length of ( 150 ± 0 . 1 ) cm .

Find the dimensional formula of Acceleration.

Find the dimensional formula of Impulse, J .

Can pressure p , density ρ and velocity v be taken as fundamental quantities?

Find the dimensional formula of Torque, T .

The surface tension of mercury is 32 dyne c m – 1 . Its value in SI units is

Given that T stands for time period and l stands for the length of simple pendulum. If S is the acceleration due to gravrty, then which of the following statements about the relation T 2 = ( l / g ) is correct?

In the relation dy dt = 2 ωsin ⁡ ωt + ϕ 0 the dimensional formula for ωt + ϕ 0 is

In the measurement of a physical quantity X = A 2 B C 1 / 3 D 3 . The percentage errors introduced in the measurements of the quantities A, B, C and D are 2%, 2%, 4% and 5% respectively. Then the minimum amount of percentage of error in the measurement of X is contributed by:

∫ dx 2 ax − x 2 = a n sin − 1 ⁡ x a − 1 . The value of n is (You may use dimensional analysis to solve the problem.)

The period of oscillation of a simple pendulum is T = 2 π L g Measured value of L is 20 cm known to 1mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist-watch of 1 s resolution. The accuracy in the determination of g is

The dimension of stopping potential V 0 in photoelectric effect in units of Planck’s constant ‘h’, speed of light ‘C’ and universal gravitational constant ‘G’ and ampere A is:

A quantity f is given by f = h c 5 G where c is speed of light, G universal gravitational constant and h is the Planck’s constant . Dimensions of f is that of:

If speed V, area A and force F are chosen as fundamental units, then the dimension of Young’s modulus will be:

The quantities x = 1 μ 0 ∈ 0 , y = E B and z = l C R are defined where C-capacitance, R-Resistance, l -length, E-Electric field, B-magnetic field and ∈ 0 , μ 0 − free space permittivity and permeability respectively. Then :

In terms of resistance (R) and time (T) the ratio μ ∈ is equal to (where μ = permeability , ∈ = permittivity)

The acceleration due to gravity is 10 ms -2 . If the units of length and time are changed to kilometer and hour respectively, the numerical value of the acceleration due to gravity is

In C.G.S. system the magnitude of the force is 100 dynes. In another system where the fundamental physical quantities are kilogram, meter and minute, the magnitude of the force is

A physical quantity is measured and its value is found to be nu where n = numerical value and u = unit. Then which of the following relations is true

Experiment shows that two perfectly neutral parallel metal plates separated by a small distance ‘d’ attract each other via a very weak force, known as the Casimir force. The force per unit area of the plates, F, depends only on the Planck constant h, on the speed of light c, and on ‘d’. Which of the following has the best chance of being correct for F?

The length of a cylinder is measured with a meter rod having least count 0.1 cm. Its diameter is measured with Vernier Calipers having least count 0.01 cm. Given that length is 5.0 cm and radius is 2.00 cm. The percentage error in the calculated value of the volume will be

A physical quantity x depends on quantities y and z as follows: x = A y + B tan ( C z ) , where A, B, and C are dimensionless constants. Which of the followings do not have the same dimensions?

The frequency f of vibrations of a mass m suspended from a spring of spring constant k is given by f = C m x k y , where C is a dimensionless constant. The values of x and y are, respectively,

The density of a material in CGS system of units is 4 g/cc. In a system of units in which unit of length is 2 cm and unit of mass is 16 g, the numerical value of density of material is: units.

In a new system of units, unit of mass is 100 g, unit of acceleration is 2 m/s 2 and unit of frequency is 4 sec -1 , in this new system of units, then the value of 10 J in this new system is

A watt is

If u 1 and u 2 are the units selected in two systems of measurement and n 1 and n 2 their numerical values, then

A screw gauge has a screw having 2 threads in 1mm. The circular scale has 50 divisions. Find the diameter of wire, if the main scale shows 6th division and the circular reads 4

Consider the expression ∫ v × d v g − b v 2 = a , in which v and g are speed and acceleration due to gravity respectively. What is the dimensional formula of ‘a’.

If the percentage errors of A. B, and C are a, b, and c, respectively, then the total percentage error in the product ABC is

The quantities A and B are related by the relation A/B = m, where m is the linear mass density and A is the force, the dimensions of B will be

The potential energy of a particle varies with distance x as U = A x 1 / 2 x 2 + B , where A and B are constants. The dimensional formula for A x B is

An experiment measures quantities a, b, and c, and then X is calculated from X = a 1 / 2 b 2 c 3 . If the percentage errors in a, b, and c are ± 1 % , ± 3 % , and ± 2 % , respectively, then the percentage error in X can be

If an unknown quantity, ϕ = m a α log ⁡ 1 + α l m a . where m = mass, a = acceleration and l = length.

A body travels uniformly a distance of ( S + Δ S ) in a time ( t ± Δ t ) . what may be the condition so that body within the error limits move with a velocity S t ± Δ S Δ t ?

The position of a particle at time r is given by the relation x ( t ) = v 0 α 1 − e − α t , where v 0 is a constant and α > 0. I The dimensions of v 0 and a are respectively

A wire has a mass 0.4 ± 0.004 g and length 8 ± 0.08 ( cm ) The maximum percentage error in the measurement of its density is 4%. The radius of the wire is r ± Δ r , find Δ r .

While measuring acceleration due to gravity by a simple pendulum, a student makes a positive error of 2% in the length of the pendulum and a positive error of 1% in the value of time period. His actual percentage error in the measurement of the value of g will be

In the relation V = π 8 P r 4 n l , where the letters have their usual meanings, the dimensions of V are

The mass of the liquid flowing per second per unit area of cross section of the tube is proportional to P x and v y , where P is the pressure difference and v is the velocity, then the relation between x and y is

Assuming that the mass rn of the largest stone that can be moved by a flowing river depends upon the velocity v of the water, its density ρ , and the acceleration due to gravity g. Then m is directly proportional to

If X = a + b, the maximum percentage error in the measurement of X will be

The moon is observed from two diametrically opposite points A and B on the earth. The angle θ subtended at the moon by the two directions of observation is 1 ∘ 54 ‘ . he distance of the moon from the earth is [Given diameter of earth = 1.276 × 10 7 m ]

The volumes of two bodies are measured to be V 1 = ( 10.2 ± 0.02 ) c m 3 a n d V 2 = ( 6.4 ± 0.01 ) c m 3 . The sum and difference in volumes with error limits is

Two resistors of resistances R 1 = 100 ± 3 Ω a n d R 2 = 200 ± 4 Ω are connected in parallel, then the equivalent resistance in parallel is (in ohm) ( U s e 1 R ‘ = 1 R 1 + 1 R 2 a n d Δ R ‘ Δ R ‘ 2 = Δ R 1 R 1 2 + Δ R 2 R 2 2 )

If L = 2.5 × 10 4 a n d B = 3.9 × 10 5 , then (B – L) is

The area enclosed by a circle of diameter 1.06 m to correct number of significant figures is

5.74 g of a substance occupies 1.2 c m 3 . Keeping the significant figure in view, its density is given by

Count total number of significant figures in the following measurement: 7 . 090 × 10 5

Count total number of significant figures in the following measurement: 10.00 cm

SI unit of Magnetic field is

Round off the following numbers to three significant figures: 24.937

The dimensions of solar constant are

When a current of ( 2.5 ± 0.5 ) A flows through a wire, it develops a potential difference of ( 20 ± 1 ) V . The resistance of wire is

The mass of a box measured by a grocer’s balance is 2.3 kg. Two gold pieces of masses 20.15 g and 20.17 g are added to the box. The total mass of the box is

The significant figures in 300.500 are

A sextant is used to measure

What is the number of significant figures in ( 3.20 + 4.80 ) × 10 5 ?

A pressure of 10 6 d y n e c m − 2 is equivalent to

If ∆ X is absolute error in the measurement of X and ∆ Y is absolute error in the measurement of Y, then maximum absolute error in the measurement of difference of X and Y is

How many significant figures are there in the numbers 108.023 and 0.19?

The pitch of a screw is 1mm and there are 100 divisions on the circular scale. In measuring the diameter of a sphere there are six divisions on the linear scale and forty divsions on circular scale coincide with the reference line. Find the diameter of the sphere.

Simplify and round to the appropriate number of significant digits: 0 . 00435 × 4 . 6

The diameter of a wire as measured by screw gauge was found to be 2.620, 2.625, 2.630, 2.628 and 2.626 cm. Express the result in terms of percentage error.

The volumes of two bodies are measured to be V 1 = ( 10 . 2 ± 0 . 02 ) cm 3 and V 2 = ( 6 . 4 ± 0 . 01 ) cm 3 . Calculate sum and difference in volumes with error limits.

The diameter of a wire as measured by screw gauge was found to be 2.620, 2.625, 2.630, 2.628 and 2.626 cm. Express the result in terms of percentage error.

The diameter of a wire as measured by screw gauge was found to be 2.620, 2.625, 2.630, 2.628 and 2.626 cm. Calculate mean absolute error.

The significant figures in the number 6.0023 are

The mass of a ball is 1 . 76 kg . The mass of 25 such balls is

The radius of a sphere is measured to be ( 2 . 1 ± 0 . 5 ) cm . Calculate its surface area with error limits.

If the random error in the arithmetic mean of 50 observations is α , then the random error in the arithmetic mean of 150 observations would be

The length of a rod is ( 11 . 05 ± 0 . 2 ) cm . What is the length of the two rods?

The respective number of significant figures for the numbers 23.023, 0.0003 and 2 . 1 × 10 – 3 are

Find the value of 525.5 + 10.81 – 53.15.

If we measure a length I = 6 . 24 cm with the help of a vernier callipers, then what is least count of vernier callipers?

The mass of a box measured by a grocer’s balance is 2 . 3 kg . Two gold pieces of masses 20 . 15 g and 20 . 17 g are added to the box. What is the total mass of the box?

If x = 10 . 0 ± 0 . 1 and y = 10 . 0 ± 0 . 1 , then 2 x – 2 y is equal to

Find the dimensional formula of Universal constant of gravitation, G .

The frequency (f) of a stretched string depends upon the tension F (dimensions of force), length l of the string and the mass per unit length μ of string. Derive the formula for frequency.

Dimension of velocity gradient is

Which of the following pairs of physical quantities does not have same dimensional formula?

If L and R denote inductance and resistance, respectively, then the dimensions of L/R are

SI unit of intensity of wave is

The damping force of an oscillating particle is observed to be proportional to velocity. The constant of proportionality can be measured in

The mass and volume of a body are 4.237 g and 2.5 c m 3 respectively. The density of material of the body in correct significant figures is.

One amu is equivalent to 931 MeV energy. The rest mass of electron is 9 . 1 × 10 – 31 k g . The mass energy is 1 a m u = 1 . 67 × 10 – 27 k g

Taking frequency f, velocity v and density r to be the fundamental quantities, then the dimensional formula for momentum will be

Which of the following pairs has same dimensions?

If p represents radiation pressure, c represents speed of light and q represents radiation energy striking a unit area per second, then non-zero integers a, b and c are such that p a q b c c is dimensionless, then

The equation of alternating current is I = I 0 e − t / C R where t is time, C is capacitance and R is resistance of coil, then the dimensions of C R is

One yard in SI unit is equal

A new unit of length is chosen such that the speed of light in vacuum is unity. Then the distance between the sun and the earth in terms of the new unit, if light takes 8 min and 20 s to cover this distance?

Which of the following is the dimension of the coefficient of friction?

Which of the following sets have different dimensions?

The length, breadth and thickness of a rectangular sheet of metal are 4.234 m, 1.005 m and 2.01 cm respectively. The area and volume of the sheet to correct significant figures are

Which of the following physical quantities has a unit but no dimensions?

What are the dimensions of electrical resistance?

The dimension of 1 2 ε 0 E 2 ( ε 0 : permittivity of free space; E: electric field) is

A simple pendulum is being used to determine the value of gravitational acceleration ‘g’ at a certain place. The length of the pendulum is 20.0 cm known to 1mm accuracy and a stop watch with 1s resolution measures the time taken for 40 oscillations to be 50s. The accuracy in g is

The unit less quantities is

The physical quantity having the same dimensional formula as that of entropy is

Torr is the unit of physical quantity

Debye is a unit of

If force ‘ F ‘ , acceleration ‘ A ‘ and time ‘ T ‘ are taken as fundamental quantities then the dimensions of energy are.

μ = A + B λ + C λ 2 is dimensionally correct the dimensions of A , B & C respectively are ( μ , A , B , C are constants where λ is wave length and μ is refractive index)

The velocity of sound in air ( v ) pressure ( p ) and density of air ( d ) are related as v α p x d y the value of ‘ x ‘ and ‘ y ‘ respectively are

The Number of significant figures in 0.0006032 is

If the length of a cylinder is measured to be 4.28cm with an error of 0.01cm, the percentage error in the measured length is nearly.

A stick has a length of 12.132cm and Another stick has a length of 12.4cm. If the two sticks are placed end to end what is their total length?

One side of a cube is measured as a = 4.03 ± 1 % what is its volume?

Of the following the dimensionless error is

The n t h division of main scale coincides with ( n + 1 ) t h division of vernier scale. Given one main scale division is equal to ‘ a ‘ units. The least count of vernier is

Find the value of 1.53 × 0.9995 1.592 with due regard for significant figures.

The least count of vernier callipers is

The Average life of an Indian is 56years. Find the number of times the human heart beats in the life of an Indian, if the heart beats once in 0.8 Second

In a screw gauge the zero of main scale coincides with fifth division of circular scale, the circular scale contains 50divisions Now a ball placed between screws, it takes four 0.5mm on main scale in one rotation and it takes four rotatory. To measure the ball then find diameter of the ball is (Index line coincides with 25line on circular scale)

The diameter of a cylinder is measured using a Vernier calipers with no zero error. If is found that the zero of the Vernier scale lies between 5.10cm and 5.15cm of the main scale. The Vernier scale has 50 divisions equivalent to 2.45cm. The 24division of the Vernier scale exactly coincides with one of the main scale divisions. The diameter of cylinder is

Express 1light year in terms of meters. What is its order of magnitude.

State the no. of significant figures in the following measurements i) 0.020800m ii) 5.308 N / m 2 iii) 1.90 × 10 11 k g

The specific resistance ρ of a thin wire of radius r = 0.26 ± 0.02 c m , resistance R = ( 32 ± 1 ) Ω and length l = 78 ± 0.01 c m . Find the percentage error in ρ is

The specific heat of a gas one measured as C P = 12.28 ± 0.2 ) units and C v = 3.97 ± 0.3 ) units find the value of percentage error of real gas constant ‘ R ‘

A simple pendulum is being used to determine the value of acceleration due to gravity ‘g’ at a certain place. The length of the pendulum is measured as 25.0 cm and a stop watch with 1s resolution measures the time taken for 40 oscillations to be 50s. The accuracy in ‘g’ is :

If the screw on a screw – gauge is given six rotations, it moves by 3 mm on the main scale. If there are 50 divisions on the circular scale the least count of the screw gauge is :

The least count of the main scale of a vernier callipers is 1mm. Its vernier scale is divided into 10 divisions and coincide with 9 divisions of the main scale. When jaws are touching each other, the 7th division of vernier scale coincides with a division of main scale and the zero of vernier scale is lying right side of the zero of main scale. When this vernier is used to measure length of a cylinder the zero of the vernier scale is between 3.1cm and 3.2cm and 4th VSD coincides with a main scale division. The length of the cylinder is (VSD is vernier scale division)

If momentum (P), area (A) and time (T) are taken to be the fundamental quantities, then the dimensional formula for energy is:

Using screw gauge of pitch 0.1 cm and 50 divisions on its circular scale, the thickness of an object is measured. It should correctly be recorded as :

Amount of solar energy received on the earth’s surface per unit area per unit time is defined as solar constant. Dimension of solar constant is :

Dimensional formula for thermal conductivity is (here K denotes the temperature) :

A quantity x is given by I F v 2 / W L 4 in terms of moment of inertia I, force F, velocity ν , work W and length L. The dimensional formula for x is same as that of:

A physical quantity z depends on four observables a , b , c and d , as z = a 2 b 2 3 c d 3 . The percentages of error in the measurement of a , b , c and d are 2 % , 1.5 % , 4 % a n d 2.5 % respectively. The percentage of error in z is:

The time period of oscillation of simple pendulum is given by T = 2 π l g where l is 100 cm and is known to have 0.1 cm accuracy. The time period is 2s. The time (t) of 100 oscillations is measured by a stop watch of least count 0.1s. The maximum percentage error in measurement of g is

The focal length of a spherical mirror from the following observations : object distance u = 50.1 ± 0.5 cm and image distance v = 20.1 ± 0.2 cm is

A physical quantity Q is related to four observables x, y, z and t by the relation Q = x 2 / 5 z 3 y t .The percentage errors of measurement in x, y, z and t are 2.5%, 2%, 0.5%, and 1% respectively. What will be percentage error in Q.

The dimensional formula of 1 2 ε 0 E 2 ( ε 0 : permittivity of free space and E : Intensity of electric field) is

The dimension of a b in the equation P = a − t 2 b x , where P is pressure, x is distance and t is time, is

From the dimensional consideration, which of the following equation is correct? T- time period G- universal gravitational constant M- mass of earth

The dimension of a b in the equation P = a – t 2 b x , where P is pressure, x is distance and t is time, is

The speed of light (c), gravitational constant (G) and Planck’s constant (h) are taken as the fundamental units in a system. The dimension of time in this system is:

With the usual notations, the following equation S t = u + 1 2 a ( 2 t − 1 ) is

The dimension of e 2 / 4 π ε 0 h c , where e , ε 0 , h and c are electric charge, electric permittivity of free space, Planck’s constant and velocity of light in vacuum, respectively, is

A physical parameter a can be determined by measuring the parameters b, c, d and e using the relation a = b α c β / d γ e δ . If the maximum errors in the measurement of b, c, d and e are b 1 % , c 1 % , d 1 % and e 1 % , then the maximum error in the value of a determined by the experiment is

In an experiment, the following observation’s were recorded: L=2.820 m, M=3.00kg, l=0.087cm, Diameter D=0.041 cm. Taking g=9.81 m/s 2 ,using the formula Y = 4 M g L π D 2 l , the maximum permissible error in Y is

To determine the Young’s modulus of a wire, the formula is Y = F A × L Δ L ; where L=length, A=area of cross-section, ∆ L= change in length of the wire when stretched with a force F. The conversion factor to change its unit from CGS to MKS system is

If x = a t + b t 2 , where x is the distance travelled by the body in kilometers while t is the time in seconds, then the unit of b is

If S = a + b t + c t 2 . S is measured in metres and t in seconds. The unit of c is

Suppose refractive index μ is given as μ = A + B λ 2 where A and B are constants and λ is wavelength, then dimensions of B are same as that of

Force F is given in terms of time t and distance x by F = A sin C t + B cos D x . Then the dimensions of A/B and C/D are

If L and R denote inductance and resistance respectively, then the dimensional formula of L/R is:

If force F, acceleration A, and time T are taken as the fundamental physical quantities, the dimensions of length on this system of units are

If C (the velocity of light) g, (the acceleration due to gravity), and P (the pressure) are the fundamental quantities in MKS system, then the dimensions of length will be same as that of

Acceleration due to gravity on the surface of the earth is g = G M R 2 . The gravitational constant G is exactly known. But percentage error in measurement of the mass of earth M and radius of the earth R are 1% and 2% respectively. The maximum percentage error in measurement of acceleration due to gravity on the surface of the earth is n%. The value of n is

If x = 0.72 + 0.8 + 3.87 – 1.089, then number of significant digits in the value of x is

If y = 2.21 x 0.3, then the number of significant digits in the value of y is .

Round off the number “3.87607” to one digit.

If unit of mass becomes 2 times, the unit of length becomes 4 times and the unit of time becomes 4 times in the unit of Planck’s constant. Due to this unit of Planck’s constant becomes times.

A stone is lying at rest in a river. The minimum mass of stone, m = k ρ v x g − 3 is needed to remain at rest. Here, k = constant having no unit, g = acceleration due to gravity, v = river flow velocity , ρ = density of water. The value of x is

If force F, velocity v and time T are taken as fundamental units. The dimension of force in the dimensional formula of pressure is

A particle of mass m is executing oscillation about origin on x-axis. Its potential energy is U ( x ) = K | X | n .If the time period T is function of its mass, amplitude (a) and (K) ; the value of n if T α a − 1 / 2 (K’ is a constant) is

The energy E of an oscillating body in simple harmonic motion depends on its mass m, frequency n and amplitude A as E = k ( m ) x ( n ) y ( A ) z The value of (x + y + z) is

A student forgot Newton’s formula for speed of sound but he remembers that there were speed (v), pressure (p) and density (d) in the formula. He then starts using dimensional analysis to find the actual relation by assuming v ∝ p x d y . The value of x – y is:

It is estimated that per second each square meter of earth receives about 1400 J of heat energy from the Sun. This is called Solar constant. The value of solar constant in some system is cal/cm 2 -min. (1 cal = 4.2 J) .

In the given equation y = A 1 − e − k t v ; t is time and v velocity. If dimensional formula of k is M x L y T z then value of x + 2 y + z is equal to

The frequency of vibration ‘ f ‘ a body of mass ‘m’ suspended from a spring of spring constant k is given by f = c m x k y , where c is a dimensionless constant. The value of x + y is

It d is the depth to which a bullet of kinetic energy K can penetrate into a human body of modulus of elasticity E. Then using the method of dimension establish a relation between d, K and E. If K = c d x E y , where c is a dimensionless constant. Modulus of elasticity = Force Area × l Δ l (where l is length and ∆ l is change in length). The value of x + y is

In a new system of units, the unit of mass is 100 g, unit of length is 4 m and unit of time is 2 s. The numerical value of 10 J in this system is

In an experiment to measure the velocity of water splash when a car passes over a water layer on the road, it is found that the velocity depends on weight of car, power delivered by its engine and thickness of water layer. If velocity of splash was found to be 3 m/s when a car weighing 1000 N passes over a layer of thickness 3 mm and its engine is supplying a power of 800 kW. Find the velocity (in m/s) of splash when car weighing 500 N passes over a layer of thickness 4 mm and its engine is supplying a power of just 400 kW.

The equation of the state of some gases can be expressed as P + a V 2 = b θ V , where P is the pressure, V the volume, θ the absolute temperature, and a and b are constants. The dimensional formula of a is

In the relation P = α β e − α Z k θ P is pressure, Z is the distance, k is Boltzmann constant and θ is the temperature. The dimensional formula of β will be

The frequency of vibration of string is given by ϑ = n 2 l F λ 1 / 2 , here p is number of segments in the string, l is the length and F is the tension in the string. The dimensional formula for λ will be

A wire has a mass 0.3 ± 0.003 g, radius 0.5 ± 0.005 mm and length 6 ± 0.06 cm. The maximum percentage error in the measurement of its density is

The dimensions of ε 0 μ 0 are

The frequency ( n ) of vibration of a string is given as n = 1 2 l T m , where T is tension and l is the length of vibrating string, then the dimensional formula of m is

If frequency F, velocity V, and density D are considered fundamental units, the dimensional formula for momentum will be

If ∫ d t 3 a t − 2 t 2 = a x sin − 1 ⁡ t 2 a 2 − 1 the value of x is

In a new system of units mass, acceleration and frequency are taken as fundamental units. If unit of mass is 100 g, unit of acceleration is 2 m/s 2 and unit of frequency is 4 sec -1 in the new system of units. Then the value of 0.1 J in this system is

Consider the expression ∫ v × d v g − b v 2 = a , in which v and g are speed and acceleration due to gravity respectively. What is the dimensional formula of ‘a’.

Consider the expression ∫ v × d v g − b v 2 = a , in which v and g are speed and acceleration due to gravity respectively. What is the dimensional formula of ‘b’.

A screw gauge with a pitch of 0.3 mm and a circular scale with 100 divisions is used to measure the thickness of a thin sheet of steel. What is the thickness of the sheet if main scale reading is 1mm and the 30 th division coincides with the main scale line. (There is no zero error)?

Write the dimensions of a x b in the relation E = b − x 2 a t where E is the energy, x is the displacement, and t is the time.

If the velocity of light C, the universal gravitational constant G, and Planck’s constant h are chosen as fundamental units, the dimensions of mass in this system are

which of the following product of e, h, μ , G (where p is the permeability) be taken so that the dimensions of the product are same as that of the speed of light?

If the velocity (V), acceleration (A), and force (F) are taken as fundamental quantities instead of mass (M) length (L), and time (T), the dimensions of Young’s modulus (Y) would be

The best method to reduce random error is

Using mass (M), length (L), time (T), and electric current (A) as fundamental quantities, the dimensions of permittivity will be

Which of the following numbers has least number of significant figures?

A length is measured as 7.60 m. This is the same as

A physical quantity X is represented by X = M x L − y T − z . The maximum percentage errors in the measurement of M, L, and T, respectively, are a%, b% and c%. The maximum percentage error in the measurement of X will be

The length l, breadth b, and thickness t of a block of wood were measured with the help of a measuring scale. The results with permissible errors (in cm) are l = 15.12 ± 0.01 , b = 10.15 ± 0.01 , and t = 5.28 ± 0.01 The percentage error in volume up to proper significant figures is

The resistance of a metal is given by R = V/I, where V is potential difference and I is the current. In a circuit, the potential difference across resistance is V = ( 8 ± 0.5 ) V and current in resistance, I = ( 4 ± 0.2 ) A . What is the value of resistance with its percentage error?

The specific resistance ρ of a circular wire of radius r, resistance R, and length l is given by ρ = π r 2 R / l . Given: r = 0.24 ± 0.02 cm , R = 30 ± 1 Ω , and l = 4.80 ± 0.01 cm The percentage error in ρ is nearly

The dimensional formula for a physical quantity x is M − 1 L 3 T − 2 .The errors in measuring the quantities M, L, and T, respectively, are 2%,3%, and 4%. The maximum percentage of error that occurs in measuring the quantity x is

The relative density of a material is found by weighing the body first in air and then in water. If the weight in air is (10.0 ± 0.1) gf and the weight in water is (5.0 ± 0.1) gf, then the maximum permissible percentage error in relative density is

The heat generated in a circuit is given by Q = I 2 R t , where I is current, R is resistance, and t is time. If the percentage erors in measuring l,R, and t are 2%, 1% and 1%, respectively, then the maximum error in measuring heat will be

A gas bubble from an expression under water, oscillates with a period T proportional to p a d b E c , where p is the static pressure, d is the density of water and E is the total energy of explosion. Find the value of a.

The wavelength associated with a moving particle depends up on p th power of its mass m, q th power of its velocity v and r th power of Planck’s constant h. Then the correct set of values of p, q and r is

In the relation P = α β e − α Z / k θ , P is the pressure, Z is the distance, k is the Boltzmann constant and q is the temperature. The dimensional formula of β will be

In a direct impact, loss in kinetic energy is given by Δ K = M 1 M 2 2 M 1 + M 2 ⋅ V 1 − V 2 2 1 − k 2 with usual notations (except k). The quantity k will have dimensional formula

If area (A) velocity (v) and density ( ρ ) are base units, then the dimensional formula of force can be represented as

A bus travels distance x 1 when accelerates from rest at constant rate a 1 for some time and after that travels a distance x 2 when decelerates at a constant rate a 2 to come to x 1 + x 2 = a 1 a 2 t 2 2 a 1 + a 2 . Choose the correct option(s).

In the formula X = 3 Y Z 2 , X and Z have dimensions of capacitance and magnetic induction respectively. what are the dimensions of Y in MKSQ system?

If F = v C ln ⁡ ( x b ) , then

A physical quantity P is given by P = A 3 B 1 / 2 C − 4 D 3 / 2 The quantity which brings in the maximum percentage error in P is

If m, e, ε 0 , h and c denote mass electron, charge of electron. Planck’s constant and speed of light, respectively. The dimensions of m e 4 ε 0 2 h 3 c are

∫ d t 2 a t − t 2 = a x sin − 1 ⁡ t a − 1 The value of x is

Number of particles is given by n = − D n 2 − n 1 x 2 − x 1 crossing a unit area perpendicular to X-axis in unit time, where n 1 and n 2 are number of particles per unit volume for the value of x meant to x 2 and x 1 . Find dimensions of D called as diffusion constant.

What is the SI unit of surface tension?

In an experimental set up, the density of a small sphere is to be determined. The diameter of the small sphere is measured with the help of a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the sphere has a relative error of 2%, the relative percentage error in the density is

A screw gauge gives the following reading, when used to measure the diameter of a wire. Main scale reading : 0 mm Circular scale reading : 52 divisions Given that 1 mm on main scale corresponds to 100 divisions of the circular scale The diameter of the wire from the above data is

A vernier calliper has 1 mm mark on the main scale. It has 20 equal divisions on the vernier scale which match with 16 main scale divisions. For this vernier callipers, the least count is

The average speed of a train is measured by 5 students. The results of measurements are given below

Object distance, u = ( 50.1 ± 0.5 ) c m and image distance v = ( 20.1 ± 0.2 ) c m , then focal length is

Calculate percentage error in determination a time period of a pendulum T = 2 π l g o r 2 π ( l g ) 1 / 2 where, l and g are measured with ± 2 % a n d ± 3 % e r r o r s .

The period of oscillation of a simple pendulum is measured, in successive measurement the readings turn out to be 2.63 s, 2.56 s, 2.42 s, 2.71 s and 2.80 s. Then, the relative error or percentage error is

The temperature of two bodies measured by a thermometer are t 1 = 20 0 C + 0.5 0 C a n d t 2 = 50 0 C ± 0.5 0 C . The error in temperature difference is

The resistance R = V I ‘ w h e r e V = ( 100 ± 5 ) V a n d I = ( 10 ± 0.2 ) A . The percentage error in R is

The period of oscillation of a simple pendulum is T = 2 π L g . Measured value of L is 20 cm known to 1mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist-watch of 1 s resolution. The accuracy in the determination of g is

Is the given expression of velocity of sound given by v = ( E ρ ) is dimensionally correct? Here, E = coefficient of elasticity, ρ = density of medium

The time period T of simple pendulum depends upon length l of the pendulum and gravitational acceleration. The formula for time period of simple pendulum is given by

Consider a simple pendulum having a bob attached to a string, that oscillates under the action of the force of gravity. Suppose that the period of oscillations of the simple pendulum depends on its length (l ), mass of the bob (m) and acceleration due to gravity (g). Using the method of dimensions, expression for its time period is

In SI system, the magnitude work done is joule. In another system, where the fundamental physical quantities are in gram, centimetre and second, the magnitude of work is

The SI unit of energy is J = k g m 2 s − 2 , that of speed v is m s − 1 and of acceleration a is m s − 2 which one of the formula for kinetic energy given below is correct on the basis of dimensional arguments. [Given m stands for the mass of body]

Given equation 1 2 m v 2 = m g h , where m is the mass of the body, v is velocity, g is the acceleration due to gravity and h is the height. Then the given equation is

The angle of 1″ (second of arc) in radians is ( G i v e n 360 0 = 2 π r a d , 1 0 = 60 ‘ a n d 1 ‘ = 60 ” )

If force F, length L and time T be considered fundamental units of mass will be

Round off the following numbers to three significant figures: 24.937

Count total number of significant figures in the following measurement: 4.07080

Round off the following numbers to three significant figures: 24572

Count total number of significant figures in the following measurement: 950kg

Nuclear cross-section is measured in barn which is equal to

The ratio of one micron to one nanometer is

The order of 2 30 is approximately

Units of magnetic flux is

Which of the following quantities has not been expressed in proper units?

What are the units of magnetic permeability?

Which of the following is a dimensional constant?

The density of a cube is measured by measuring its mass and length of its sides. If the maximum errors in the measurement of mass and length are 3% and 2% respectively, then the maximum error in the measurement of density is

A quantity is represented by M a L b T c . The percentage error in measurement of M, L, and T are α % , β % a n d γ % respectively. The percentage error in X would be

Which of the following numerical values have three significant figures?

Subtract 0.2 J from 7.26 J and express the result with correct number of significant figures.

The sum of numbers 436.32, 227.2 and 0.301 in appropriate significant figures in

Which of the following cannot be regarded as an essential characteristic of a unit of measurement?

Young modulus of steel is 1.9 × 10 11 N / m 2 . When expressed in CGS units of d y n e / c m 2 , it will be equal to ( 1 N = 10 5 d y n e , 1 m 2 = 10 4 c m 2 )

Which of the following pairs have the same dimensions?

The smallest division on main scale of a Vernier calipers is 1 mm and 10 Vernier divisions coincide with 9 main scale divisions. While measuring the length of a wire, the zero mark of the Vernier scale lies between 10.2 cm and 10.3 cm and third division of Vernier scale coincides with a main scale division. Find the length of the wire

The velocity v of a particle at time t is given by the equation v = at + b t + c . The dimensions of a, b, c are respectively

A new system is formed such that it uses force, energy and velocity as fundamental quantities with units 20N, 200J and 5 ms -1 . Calculate the unit of mass ( in kg) in this new system

The rate of flow (V) of a liquid (coefficient of viscosity is η ) flowing through a pipe of radius r , length L and pressure gradient p is given by Poiseuille’s equation V = π 8 r x η z L p y . Then calculate the value of x.

Round off the following numbers to three significant figures: 42 . 450 × 10 9

Round 742396 to four, three and two significant digits.

Find, volume of a cube of side a = 1 . 4 × 10 – 2 m .

Radius of a wire is 2.50 mm. The length of the wire is 50.0 cm If mass of wire was measured as 25 g, then find the density of wire in correct significant figures. Given, π = 3 . 14 , exact

Round to the appropriate number of significant digits: 13.214+234.6+7.0350+6.38

Round to the appropriate number of significant digits: 1247+134.5+450+78

The diameter of a wire as measured by screw gauge was found to be 2.625, 2.630, 2.628 and 2.626 cm. Calculate mean absolute error in each measurement.

The diameter of a wire as measured by screw gauge was found to be 2.620, 2.625, 2.630, 2.628 and 2.626 cm. Calculate mean value of diameter.

The diameter of a wire as measured by screw gauge was found to be 2.620, 2.625, 2.630, 2.628 and 2.626 cm. Express the result in terms of percentage error.

Calculate percentage error in determination of time period of a pendulum T = 2 π l g where l and g are measured with ± 1 % and ± 2 % .

The mass and density of a solid sphere are measured to be ( 12 . 4 ± 0 . 1 ) kg and ( 4 . 6 ± 0 . 2 ) kg / m 3 . Calculate the volume of the sphere with error limits.

Round off 231.45 to four, three and two significant digits.

Three measurements are, a = 25 . 6 , b = 21 . 1 a n d c = 2 . 43 . Find the value a – b – c to correct significant figures.

A thin wire has a length of 21.7 cm and radius 0.46 mm. Calculate the volume of the wire to correct significant figures.

The number of significant figures in 3400 is

Calculate equivalent resistance of two resistors R 1 and R 2 in parallel where, R 1 = ( 6 ± 0 . 2 ) ohm and R 2 = ( 3 ± 0 . 1 ) ohm .

The radius of a sphere is measured to be ( 1 . 2 ± 0 . 2 ) cm . Calculate its volume with error limits.

Find the value of 3 . 008 × 38 . 8 2 . 8768 .

The length and breadth of a metal sheet are 3.124 m and 3.002 m, respectively. The area of this sheet upto correct significant figure is

Which of the following measurement is most accurate?

A student measures the thickness of a human hair by looking at it through a microscope of magnification 100. He makes 20 observations and finds that the average width of the hair is 3 . 5 mm . What is thickness of the hair?

In Ohm’s law experiment, the reading of voltmeter across the resistor is 12 . 8 V and current through resistor is 0 . 30 A . Find the resistance of resistor.

The density of a cube is measured by measuring its mass and length of its sides. If the maximum error in the measurement of mass and length are 4 % a n d 3 % respectively, the maximum error in the measurement of density will be

If error in measuring diameter of a circle is 4%, the error in measuring radius of the circle would be

A body travels uniformly a distance of ( 13 . 8 ± 0 . 2 ) m in a time ( 4 . 0 ± 0 . 3 ) s . The velocity of the body within error limit is

A body of mass m = 3 . 513 kg is moving along the X-axis with a speed of 5 . 00 ms – 1 . The magnitude of its momentum is recorded as

If error in measurement of radius of a sphere is 1 % , what will be the error in measurement of volume?

The radius of a ball is ( 5 . 2 ± 0 . 2 ) cm . The percentage error in the volume of the ball is approximately

The length of a simple pendulum is about 100 cm known to have an accuracy of 1 mm . Its period of oscillation is 2 s determined by measuring the time for 100 oscillations using a clock of 0 . 1 s resolution. What is the accuracy in the determined value of g?

A thin wire has length of 21 . 7 cm and radius 0 . 46 mm . Calculate the volume of the wire to correct significant figures.

The least count of a stop watch is 0 . 2 s . The time of 20 oscillations of a pendulum is measure to be 25 s . The percentage error in the time period is

A cube has a side of length 2 . 342 m . Find the surface area and volume in correct significant figures.

Two gold pieces of masses are 20 . 15 g and 20 . 17 g . What is the difference in the masses of the pieces to correct significant figures?

Find density when a mass of 9 . 23 kg occupies a volume of 1 . 1 m 3 . Take care of significant figures,

The period of oscillation of a simple pendulum is T = 2 π L / g . Measured value of L is 20 . 0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wrist watch of 1s resolution. What is the accuracy in the determination of g?

The resistance R = V I , where V = ( 100 ± 5 . 0 ) V and I = ( 10 ± 0 . 2 ) A . Find the percentage error in R.

The temperature of two bodies measured by a thermometer are ( 20 ± 0 . 5 ) ° C and ( 50 ± 0 . 5 ) ° C . Calculate the temperature difference with error limits.

If we measure a length I = 6 . 24 cm with the help of a vernier callipers, then how many significant figures are there in the measured length?

If we measure a length l = 3 . 267 cm with the help of a screw gauge, then what is maximum uncertainty or maximum possible error in l ?

If we measure a length I = 3 . 267 cm with the help of a screw gauge, then which digits are absolutely correct and which is/are doubtful?

Find the dimensional formula of Velocity.

Find the dimensional formula of density.

Find the dimensional formula of Force.

Find the dimensional formula of Momentum.

Find the dimensional formula of Surface Tension, T .

Find the dimensional formula of Power.

Find the dimensional formula of Pressure.

The value of gravitation constant is G = 6 . 67 × 10 – 11 N · m 2 / kg 2 in SI units. Convert it into C G S system of units.

The velocity v of a particle depends upon the time t according to the equation, v = a + b t + c d + t . Write the dimensions of a , b , c a n d d .

Find the dimensional formula of coefficient of viscosity η .

Find the dimensional formula of charge q .

Find the dimensional formula of potential V .

Write the dimensions of a and b in the relation, P = b – x 2 a t , where P is power, x is distance and t is time.

Find the dimensional formula of resistance, R .

Find the dimensional formula of capacitance C .

The centripetal force F acting on a particle moving uniformly in a circle may depend upon mass m , velocity v and radius r of the circle. Derive the formula for F using the method of dimensions.

Force acting on a particle is 5 N . If units of length and time are doubled and unit of mass is halved then find the numerical value of force in the new system of units.

The dimensional formula for Planck’s constant and angular momentum are

If velocity, time and force were chosen as basic quantities, find the dimensions of mass and energy.

The viscous force F on a sphere of radius a moving in a medium with velocity v is given by F=6 π η a v . The dimensions of η are

A force is given by F = a t + b t 2 , where t is the time. The dimensions of a and b are

In the relation y = r sin ω t – k x , the dimensional formula of ω / k are

One light year is defined as the distance travelled by light in one year. The speed of light 3 × 10 8 m s – 1 . The same in metre is

If the acceleration due to gravity is 10 m s – 2 and the units of length and time are changed in kilometre and hour respectively, the numerical value of acceleration is

The equation of the stationary wave is y = 2 Asin ⁡ 2 πct λ cos ⁡ 2 πx λ Which of the following statements is wrong?

Of the following quantities, which one has the dimensions different from the remaining three?

N divisions on the main scale of a vernier callipers coincide with N + 1 divisions on the vernier scale. If each division on the main scale is of a units determine the least count of the instrument.

In the diagram shown in figure, find the magnitude and nature of zero error.

The smallest division on main scale of a vernier callipers is 1 mm and 10 vernier divisions coincide with 9 main scale divisions. While measuring the length of a line, the zero mark of the vernier scale lies between 10 . 2 cm and 10 . 3 cm and the third division of vernier scale coincides with a main scale division. Determine the least count of the callipers.

The main scale of a vemier callipers reads 10 mm in 10 divisions. Ten divisions of vemier scale coincide with nine divisions of the main scale. When the two jaws of the callipers touch each other, the fifth division of the vernier coincides with 9 main scale divisions and the zero of the vernier is to the right of zero of main scale, when a cylinder is tightly placed between the two jaws. the zero of the vernier scale lies slightly to the right of 3 . 2 cm and the fourth vernier division coincides with a main scale division. Find diameter of the cylinder.

The pitch of a screw gauge is 1 mm and there are 100 divisions on circular scale. When faces A and B are just touching each other without putting anything between the studs 32 nd division of the circular scale coincides with the reference line. When a glass plate is placed between the studs, the linear scale reads 4 divisions and the circular scale reads 16 divisions. Find the thickness of the glass plate. Zero of linear scale is not hidden from circular scale when A and B touches each other.

In a Vernier calipers, N divisions of the main scale coincide N + m divisions of the Vernier scale. What is the value of m for which the instrument has minimum least count?

Read the screw gauge shown below in the figure. Given that circular scale has 100 divisions and in one complete rotation the screw advances by 1 mm .

The pitch of a screw gauge having 50 divisions on its circular scale is 1 mm . When the two jaws of the screw gauge are in contact with each other, the zero of the circular scale lies 6 divisions below the line of graduation. When a wire is placed between the jaws, 3 linear scale divisions are clearly visible while 31st division on the circular scale coincides with the reference line. Find diameter of the wire.

The physical quantity having the dimensions M – 1 L – 3 T 3 A 2 is

The dimensional formula for magnetic flux is

Choose the wrong statement.

Using mass ( M ), length ( L ), time ( T ) and current ( A ) as fundamental quantities, the dimension of permeability is

The ratio of the dimensions of Planck’s constant and that of the moment of inertia is the dimension of

If the energy ( E ), velocity ( v ) and force ( F ) be taken as fundamental quantities, then the dimensions of mass will be

Given that y = A sin 2 π λ ( c t – x ) where y and x are measured in meters. Which of the following statements is true?

In the formula X = 3 Y Z 2 , X and Z have dimensions of capacitance and magnetic induction respectively. What are the dimensions of Y in M K S Q system?

Which of the following sets cannot enter into the list of fundamental quantities in any system of units?

The quantity X is given by ε 0 L Δ V Δ t , where ε 0 is the permittivity of free space, L is a length, Δ V is potential difference and Δ t is time interval. The dimensional formula for X is the same as that of

In the relation p = α β e – a z k θ , p is pressure, Z is distance, k is Boltzmann constant and θ is the temperature. The dimensional formula of β will be

Joule × second is the unit of

Which of the following is not the units of surface tension?

Which of the following is not equal to watt?

In a certain observation made to measure the length of wire and radius of bob of a simple pendulum we got, l = 23 . 2 cm , r = 1 . 32 cm and time taken for 10 oscillations was 10.0 s. Find, maximum percentage error in determination of ‘ g ‘

The dimensional formula for thermal resistance is

A new unit of length is chosen such that the speed of light in vacuum is unity. What is the distance between the sun and the earth in terms of the new unit, if light takes 8 min and 20 s to cover this distance?

If p represents radiation pressure, c represent speed of light and Q represents radiation energy striking a unit area per second, then non-zero integers x , y a n d z such that p x Q y c z is dimensionless are

ML 2 T – 3 A – 1 is the dimensional formula for

The units of length, velocity and force are doubled. Which of the following is the correct change in the other units?

The dimensional representation of specific resistance in terms of charge Q is

Dimensions of ‘ohm’ are same as

If y represents pressure and x represents velocity gradient, then the dimensions of d 2 y d x 2 are

The pairs of physical quantities that have not the same dimensions is (are)

If E = energy, G = gravitational constant, I = impulse and M = mass then dimensions of G I M 2 E 2

The density of a material in CGS system of units is 4 g / cm 3 . In a system of units in which unit of length is 10 cm and unit of mass is 100 g , the value of density of material will be

If m , e , ε 0 , h a n d c denote mass of electron, charge of electron, Planck’s constant and speed of light, respectively. The dimensions of m e 4 ε 0 2 h 3 c are

Which of the following is not the S I unit of the inductance

The dimensions of the quantities in one (or more) of the following pairs are the same. Identify the pair ( s ).

Let ε 0 denote the dimensional formula of the permittivity of the vacuum and ε 0 that of the permeability of the vacuum. If M = mass, L =length, T = time and I = electric current, then

Surface tension of water in the CGS system is 72 dyne/cm. What is its value in SI units?

A gas bubble, from an explosion under water oscillates with a period T proportional to p a d b E c where p is static pressure, d is the density of water and E is the total energy of the explosion. Find the values of a , b a n d c .

L. C and R represent the physical quantities inductance, capacitance and resistance respectively. The combinations which does not have the dimensions of frequency are

Young’s modulus of steel is 2 . 0 × 10 11 N / m 2 . Express it in dyne/cm 2 .

For n moles of gas, van der Waals’ equation is p + a V 2 ( V – b ) = n R T Find the dimensions of a a n d b , where p = pressure of gas, V = volume of gas and T = temperature of gas.

The energy E of an oscillating body in simple harmonic motion depends on its mass m , frequency n and amplitude a . Using the method of dimensional analysis, find the relation analysis, find the relation between E , m , n a n d a .

In the formula, p = n R T V – b e a R T V , find the dimensions of a a n d b , where p = pressure, n = number of moles, T = temperature, V = volume and R = universal gas constant.

Assertion: If two physical quantities have same dimensions, then they can be certainly added or subtracted. Reason: If the dimensions of both the quantities are same, then both the physical quantities should be similar.

α t 2 = F v + β x 2 . Find the dimension formula for [ α ] and [ β ] (here t = time, F = force, v = velocity, x = distance )

To find index error (e) distance between object needle and pole. of the concave mirror is 20 cm. The separation between the indices of object needle and mirror was observed to be 20.2 cm. In some observation, the observed image distance is 20.2 cm and the object distance is 30.2 cm. Find the index error e.

Assertion: Method of dimension cannot be used for deriving formulae containing trigonometrical ratios. Reason: This is because trigonometrical ratios have no dimensions.

Taking force F , length L and time T to be the fundamental quantities, find the dimensions of density.

In the equation ∫ d x 2 a x – x 2 = a n sin – 1 x a – 1 . Find the value of n .

Assertion: When we change the unit of measurement of a quantity, its numerical value changes. Reason: Smaller the unit of measurement smaller is its numerical value.

Let x a n d a stand for distance. Is ∫ d x a 2 – x 2 = 1 a sin – 1 a x dimensionally correct?

Assertion: Velocity, volume and acceleration can be taken as fundamental quantities. Reason: All the three are independent from each other.

For positive error, the correction is

Select the incorrect statement.

1 cm of main scale of a vernier calipers is divided into 10 divisions. The least count of the calipers is 0 . 005 cm , then the vernier scale must have

The vernier constant of a vernier callipers is 0 . 001 cm . If 49 main scale divisions coincide with 50 vernier scale divisions, then the value of 1 main scale division is

1 cm on the main scale of a vernier callipers is divided into 10 equal parts. If 10 divisions of vernier coincide with 8 small divisions of main scale, then the least count of the calliper is

Each division on the main scale is 1 mm . Which of the following vernier scales give vernier constant equal to 0 . 01 mm ?

A vernier calipers having 1 main scale division = 0 . 1 cm is designed to have a least count of 0 . 02 cm . If n be the number of divisions on vernier scale and m be the length of vernier scale, then

The length of a rectangular plate is measured by a meter scale and is found to be 10 . 0 cm . Its width is measured by vernier callipers as 1 . 00 cm . The least count of the meter scale and vernier callipers are 0 . 1 cm and 0 . 01 cm , respectively. Maximum permissible error in area measurement is

The length of a strip measured with a metre rod is 10 . 0 cm . Its width measured with a vernier calipers is 1 . 00 cm . The least count of the metre rod is 0 . 1 cm and that of vernier calipers 0 . 01 cm . What will be error in its area?

The length of cylinder is measured with a metre rod having least count 0 . 1 cm . Its diameter is measured with vernier callipers having least count 0 . 01 cm . Given that length is 5 . 0 cm and radius is 2 . 0 cm . The percentage error in the calculated value of the volume will be

The diameter of a cylinder is measured using a vernier callipers with no zero error. It is found that the zero of the vernier scale lies between 5 . 10 cm and 5 . 15 cm of the main scale. The vernier scale has 50 division equivalent to 2 . 45 cm . The 24 th division of the vernier scale exactly coincides with one of the main scale divisions. The diameter of the cylinder is

A vernier calliper is having 1 main scale division = 1 mm . Ten divisions of vernier scale coincide. with nine divisions of main scale. If two jaws of instrument touch each other, the 8 th division of vernier scale coincide with a mark of main scale and the zero of the vernier scale lies to the right of the zero of main scale. While measuring the length of cylinder, the zero of the vernier seale lies slightly to the left of 3 . 2 cm and the fourth vernier division coincides with a mark of the length cylinder is

A vernier callipers having main scale of 10 cm containing 100 divisions. If n be number of divisions on vernier scale of length l. Vernier calliper is designed to have a least count of 0 . 02 cm , then

The distance moved by the screw of a screw gauge is 2 mm in four rotations and there are 50 divisions on its cap. When nothing is put between its jaws, 20th division of circular scale coincides with reference line and zero of linear scale is hidden from circular scale when two jaws touch each other or zero of circular scale is lying above the reference line. When plate is placed between the jaws, main scale reads 2 divisions and circular scale reads 20 divisions. Thickness of plate is

Screw gauge is said to have a negative error

Which of the following is the most precise device for measuring length?

In four complete rotations, the distance moved by the screw on the linear scale is 2 mm . circular scale contains 50 divisions. Find the least count of the screw gauge

Least count of screw gauge is defined as

In five complete rotations, the distance moved by screw on a linear scale is 0 . 5 cm . There are 100 divisions on circular scale. While measuring the thickness of a metal plate by the screw gauge, there are five divisions on the main scale and 35 divisions coincide with the reference line. Calculate the thickness of metal plate,

The value of universal gas constant is R = 8.3 J/ k-mol. The value of R in atmosphere litre per kelvin per mol

Electron-volt is the unit of energy 1 e V = 1 . 6 × 10 – 19 J . In H-atom, the binding energy of electron in first orbit is 13.6 eV. The same in joule (J) is

The fundamental unit, which has the same power in the dimensional formulae of surface tension and coefficient of viscosity is

What is the power of a 100 W bulb in CGS units?

∫ d x 2 a x − x 2 = a n sin − 1 ( x a − 1 ) . The value of n is

If the units of M and L are increased three times, then the unit of energy will be increased by

The expression for centripetal force (F) depends upon mass of body (m), speed (v) of the body and the radius (r) of circular path will be expression for centripetal force

A suitable unit for gravitational constant is

If L denotes the inductance of an inductor through which a current I is flowing, then the dimensional formula of L I 2 is

How many wavelengths of K r 86 are there in one metre?

Farad is not equivalent to

In the equation y = a sin ( ω t + k x ) , the dimensional formula of ω is

The dimensional formula of magnetic permeability is

[ M L − 2 T − 2 ] represents dimensional formula of which of the following physical quantities?

The period of a body under SHM is respected by T = p a D b S c , where p is pressure, D is density and S is surface tension. The value of a, b and c are

The dimensions of emf in MKS is

The physical quantity which has the dimensional formula [ M 1 T − 3 ] is

Force constant has same dimensions as

The dimensional formula of the ratio of angular to linear momentum is

The maximum static friction on a body is F = μ N . Here, N = normal reaction force on the body μ = coefficient of static friction. The dimensions of μ are

If I is the moment of inertia and ω the angular velocity, what is the dimensional formula of rotational kinetic energy

A gas bubble from an explosion under water oscillates with a time period T, depends upon static pressure p, density of water r and the total energy of explosion E. The expression for the time period T. (where, k is a dimensionless constant) is

Solar constant is defined as energy received by earth per c m 2 per minute. The dimensions of solar constant are

A student measured the diameter of a small steel ball using a screw gauge of least count 0.001 cm. The main scale reading is 5 mm and zero of circular scale division coincides with 25 divisions above the reference level. If screw gauge has a zero error of -0.004 cm, the correct diameter of the ball is

The respective number of significant figures for the numbers 6.320, 6.032, 0.0006032 are

Which of the following relations for the displacement of a particle undergoing simple harmonic motion is not correct dimensionally?

A physical quantity P is described by the relation P = a 1 / 2 b 2 c 3 d − 4 . If the relative errors in the measurement of a, b, c and d respectively, are 2%,1%, 3% and 5%, then the percentage error in P will be %

The equation of state of a gas is given by P + a V 3 V − b 2 = cT , where P, V, T are pressure, volume and temperature respectively, and a, b, c are constants. The dimensions of a and b are respectively

A new system of units is proposed in which unit of mass is α kg, unit of length is β m and unit of time is γ s. What will be value of 5J in this new system?

In the formula, a = 3 b c 2 , a and c have dimensions of electric capacitance and magnetic induction respectively. What are dimensions of b in MKS system?

Electric displacement is given by D = ε E , Here, ε = electric permittivity E = electric field strength The dimensions of electric displacement are

The work done by a battery is W = ε Δ q , where Δ q charge transferred by battery, ε = emf of the battery. What are dimensions of emf of battery?

The radius of the sphere is (4.3 ± 0.1) cm. The percentage error in its volume is

The equation of current is given by the equation I = I 0 e − t / CR where t is time, C is capacitance and R is resistance of coil, then the dimensions of CR is

Calculate percentage error in determination a time period of a pendulum T =2 π l g or 2 π l g 1 / 2 where, l and g are measured with ± 2% and ± 3% errors.

Two resistors of resistances R 1 = 100 ± 3 Ω and R 2 = 200 ± 4 Ω are connected in parallel, then the equivalent resistance in parallel is (in ohm) Use 1 R ‘ = 1 R 1 + 1 R 2 and ΔR ‘ ΔR ‘ 2 = ΔR 1 R 1 2 + ΔR 2 R 2 2

An experiment measures quantities a, b, and c, and then X is calculated from X = a 1 / 2 b 2 c 3 . If the percentage errors in a, b, and c are ± 1 % , ± 3 % , and ± 2 % , respectively, then the maximum percentage error in X can be

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