Two bodies of masses 1 kg and 2 kg are moving in two perpendicular direction with velocities 1 m/s and 2 m/s as shown in figure. The velocity of the centre of mass (in magnitude) of the system will be:

Two blocks of masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse give a velocity of 14 m/s to the heavier block in the direction of lighter block. The velocity of centre of mass is

A circular disc of radius R is removed from a bigger circular disc of radius 2R, such that the circumference of the discs coincide. The centre of mass of the new disc is aR from the centre of the bigger disc. The value of a is

Five uniform circular plates, each of diameter b and mass m are laidout in a pattern shown. Using the origin shown, find the y co-ordinate of the centre of mass of the five plate system.

Two particles A and B having masses m and 3m are initially at rest at a separation 4m. They start moving towards each other under the influence of mutual gravitational force of attraction. After some time, if displacement of A is 0.1 m, then magnitude of displacement of B at that instant is

Three identical masses are kept at the corners of an equilateral triangle ABC under the action of mutual force of attraction, A moves towards B with a speed V, B moves towards C with speed V, and C moves towards A with same speed V. Then the speed of centre of mass of the system of particles is

A wagon of 200 kg is moving on a smooth track with velocity of 2 m/sec. A man of 80 kg also runs in the wagon with a velocity such that speed of the centre of mass of the system is zero. Find the velocity of man relative to the wagon (in m/s).

Two masses m 1 = 1 kg and m 2 = 2 kg and connected by a light inextensible string and suspended by means of a weightless pulley as shown in the figure. Assuming that both the masses start from rest, the distance travelled by the centre of mass in two seconds is (Take g = 10 ms – 2 )

Three particles, each of mass m are placed at the vertices of a right angled triangle as shown in figure. The position vector of the centre of mass of the system is (O is the origin and i ^ , j ^ , k ^ are unit vectors) [EAMCET 2013]

Choose the wrong statement

Two blocks of masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse give a velocity of 14 m/s to the heavier block in the direction of the lighter block. The velocity of center of mass is

A body falling vertically downwards under gravity breaks in two parts of unequal masses. The center of mass of the parts taken together shifts horizontally towards

A wedge shaped block 'A' of mass M is at rest on a smooth horizontal surface. A small block 'B' of mass 'm' placed at the top edge of inclined plane of length 'L' as shown in the figure. By the time, the block 'B' reaches the bottom end, the wedge A moves a distance of

Particles of masses 100 and 300 gram have position vectors and . Position vector of their centre of mass is

A Hollow sphere is filled with water. Which of the following points is the position of C.M. of the system shown in fig

A thin uniform rod of length L is bent at its mid point as shown in the figure. The distance of centre of mass form the point ‘O’ is

Three particles of masses 8 kg, 4 kg and 4 kg situated at (4,1), (–2,2) and (1,–3) are acted upon by external forces and . The acceleration of centre of mass of the system is

A child sits stationary at one end of a long trolley moving uniformly with a speed V on a smooth horizontal floor. If the child gets up and runs about on the trolley in any manner, what is the speed of the CM of the (trolley + child) system ?

The C.M of a uniform card board cut in ‘T’ shape as shown in figure is

A uniform square sheet has a side length of 2R. A circular sheet of maximum possible area is removed from one of the quadrants of the square sheet. The distance of centre of mass of the remaining portion from the centre of the original sheet is

An object comprises of a uniform ring of radius R and its uniform chord AB (not necessarily made of the same material) as shown. Which of the following cannot be the centre of mass of the object?

Three particles, each of mass m, are placed at the corners of a right angled triangle as shown in figure. If OA = a and OB = b, The position vector of the centre of mass is

Statements : a) The motion of the centre of mass can be studied using kepler's laws of motion. b) The internal forces will not effect the motion of the centre of mass

P is the centre of mass of a system of four point masses A, B, C and D, which are coplanar but not collinear a) P may or may not coincide with one of the point masses b) P must lie within or on the edge of at least one of the triangles formed by taking A, B, C and D three at a time c) P must lie on a line joining two of the points A, B, C, D d) P lies out side the quadrangle ABCD

A uniform disc of diameter R/2 is put over another uniform disc of diameter R of same thickness and density. The peripheries of the two discs touch each other. The centre of mass of the system from centre of big disc is

Two particles of equal mass have velocities v 1 = 4 i ^ and v 2 = 4 j ^ m/sec. First particle has an acceleration a 1 = ( 5 i ^ + 5 j ^ ) m s – 2 while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a path of

Two particles of masses 10kg and 30kg are lying on a straight line. The 10kg mass is shifted towards the 30kg mass by a distance of 2cm. By what distance should the 30kg mass be shifted so that the position of their centre of mass does not change

A ladder is leaned against a smooth wall and it is allowed to slip on a frictionless floor. Which figure represents trace of its centre of mass.

If the distance between the centres of the atoms of potassium and bromine in KBr molecule is 0.282 × 10 -9 m, the distance of centre of mass of this two particle system from potassium is (mass of bromine = 80 u and of potassium = 39 u).

Centre of mass of three particles of masses 1 kg, 2 kg and 3 kg lies at the point (1, 2, 3) and centre of mass of another system of particles 3 kg and 2 kg lies at the point (-1, 3, -2). Where should we put a particle of mass 5 kg so that the centre of mass of entire system lies at the centre of mass of first system?

The velocities of two particles A and B of same mass are V A = a i ⏞ and V B = b j ⏞ where a and b are constants. The acceleration of particle A is ( 2 a i ⏞ + 4 b j ⏞ ) and acceleration of particle B is ( a i ⏞ – b j ⏞ ) ( in m / s 2 ) . The centre of mass of two particle will move in:

An isolated particle of mass rn is moving in a horizontal plane (x-y) along the X-axis. At a certain height above the ground, it suddenly explodes into two fragments of masses m 4 and 3 m 4 . An instant later, the smaller fragment is at Y = +15 cm. The larger fragment at this instant is at:

A uniform meter stick is placed vertically on a smooth horizontal surface and released. As the stick is in motion, the center of mass moves

Half of the rectangular plate shown in figure is made of a material of density ρ 1 and the other half of density ρ 2 . The length of the plate is L. The centre of mass of the system from O is

Find the position of centre of mass of a uniform disc of radius R from which a hole of radius r is cut out. The centre of the hole is at a distance R 2 from the centre of the disc.

What will be the position of centre of mass of a half disc shown?

Two blocks of equal mass are tied with a light string which passes over a massless pulley as shown in figure. The magnitude of acceleration of centre of mass of both the blocks is (neglect friction every where):

Masses of 2 kg each are placed at the corners B and A of a rectangular plate ABCD as shown in the figure. A mass of 8 kg has to be placed on the plate so that the centre of mass of the system should be the centre O. Then the mass should be placed at:

A brick of length L is placed on the horizontal floor. The bricks of same length and size are placed on this brick, one above the other by providing a margin of L 8 from the edge of the brick placed just below, in the same direction Find the correct option:

A square of side a and uniform thickness is divided into four equal parts. If upper right part is removed, then find the coordinates of centre of mass of remaining part.

A ball of mass 1kg is thrown vertically upwards from a building with a speed of 10m/s, and another ball of mass 3kg is dropped from the same point towards the ground with the same speed. At what time will the centre of mass have the maximum height w.r.t the ground? Assume balls are left at t=0.

At t = 0, the positions and velocities of two particles are as shown in the figure. They are kept on a smooth surface and being mutually attracted by gravitational force. Find the position of centre of mass at t = 2s.

In a system of particles 8 kg mass is subjected to a force of l6 N along +ve x-axis and another 8 kg mass is subjected to a force of 8 N along +ve y-axis. The magnitude of acceleration of centre of mass and the angle made by it with x-axis are given respectively by:

The x, y coordinates of the centre of mass of a uniform L-shaped lamina of mass 3 kg is

If the net external force acting on the system of particles is zero, then the quantity which may vary is

A rigid body consists of a 3kg mass located at r 1 = ( 2 i ^ + 5 j ^ ) m and a 2kg mass located at r 2 = ( 4 i ^ + 2 j ^ ) m The position of centre of mass is

For the system of two particles co-ordinates of centre of mass are:

A body of mass m 1 = 4 kg moves at 5 i ^ ms – 1 and another body of mass m 2 = 2 kg moves at 10 i ^ ms – 1 . The kinetic energy of centre of mass is

From a circular disc of radius R, a square is cut out with a radius as its diagonal. The centre of mass of remaining portion is at a distance (from the centre)

Two persons of masses 55 kg and 65 kg respectively are at the opposite ends of a boat. The length of the boat is 3 m and weighs 100 kg. The 55 kg man walks up to the 65 kg man and sits with him. If the boat is in still water, the centre of mass of the system shifts by

Two semicircular rings of linear mass density λ and 2 λ and of radius R are joined to form a complete ring. The distance of the center of mass of the complete ring from its centre is

A particle of mass 200 g is dropped from a height of 50 m and another particle of mass 100 g is simultaneously projected up from the ground along the same line, with a speed of 100 m/s. The acceleration of the center of mass after 1 second is

A body of mass(4m) is lying in x–y plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass (m) move perpendicular to each other with equal speeds ( ν ). The total kinetic energy generated due to explosion is

A rope of length 30 cm is on a horizontal rough table with maximum length hanging from edge ‘A’ of the table. The coefficient of friction between rope and table is 0.5. The distance of centre of mass of the rope from ‘A’ is

Period of small oscillation in the two cases shows in the figure is T 1 and T 2 respectively, then (neglect viscous force)

A stationary body explodes into four identical fragments such that three of them flyoff mutually perpendicular to each other, each with same K.E., E 0 . The energy released in the explosion is

Two identical bricks of length L are piled one on top of the other on a table as shown in the figure. The maximum distance S the top brick can overhang the table with the system still balanced is:

With respect to a frame fixed to the centre of mass of a two particle system, some statements are given in following options. Select the correct statement if the particles don’t have same velocity w.r.t. an inertial frame.

Two spherical bodies of mass M and 5 M and radii R and 2 R are released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is

Two particles of mass 5kg and 10kg respectively are attached to the two ends of a rigid rod of length 1m with negligible mass. The centre of mass of the system from the 5kg particle is nearly at a distance of

Three identical spheres, each of mass M, are placed at the corners of a right angle triangle with mutually perpendicular sides equal to 2 m (see figure). Taking the point of intersection of the two mutually perpendicular sides as the origin, find the position vector of centre of mass.

Of the following choose the wrong statement

Three particles of masses 1 kg, 2kg and 3kg are situated at the corners of an equilateral triangle of side b. The coordinates of the centre of mass are (x -axis along line joining 1kg and 2kg with origin at 1 kg mass)

A body initially at rest, breaks up into two pieces of masses 2 M and 3 M respectively, together having a total kinetic energy E. The piece of mass 2 M, after breaking up, has a kinetic energy :

A stationary particle explodes into three fragments. Momentum of two fragments are P 1 = 4 i ^ + 3 j ^ k g − m / s a n d P 2 = − i ^ + j ^ k g − m / s . Then magnitude of momentum of the third particle is

In the shown figure wedge of mass M has a semicircular groove of radius R. A particle of mass m is released from A. It slides on the smooth circular track and starts climing on the right face. If M = 2m, find the velocity of the wedge at θ = 60 0 .

If a man of mass M jumps to the ground from a height ‘h’ and his centre of mass moves a distance ‘x’ after his feet strikes the ground. The average force acting on him is

Two blocks A and B are connected by a massless string. A force of 30 N is applied on block B. The distance travelled by the centre of mass in 2 sec starting from rest is

A trolley is moving horizontally with a velocity of v m/s w.r.t. earth. A man starts running in the direction of motion of trolley from one end of the trolley with a velocity 1.5 v m/s w.r.t. the trolley. After reaching the opposite end, the man turns back and continues running with a velocity of 1.5 v m/s w.r.t. trolley in the backward direction. If the length of the trolley is L, then the displacement of the man with respect to earth, measured as a function of time, will attain a maximum value of

A man of mass 80 kg is riding on a small cart of mass 40 kg which is rolling along a level floor at a speed of 2 m/s. He is running on the cart so that his velocity relative to the cart is 3 m/s in the direction opposite to the motion of cart. What is the speed of the centre of mass of the system

A particle of mass 2 gm is placed at point A(-6 cm, 0), a second particle of mass 4 gm is placed at point (3 cm, 0). A third particle of mass m is placed at the origin O. What should be the value of ‘m’ so that centre of mass of the system lies at the origin?

A raft of mass 30 kg and length 5m is floating on water. A man of mass 60 kg is standing on the raft at one end. If the man starts walking towards the other end of the raft with a velocity of 2 m/s relative to the raft, what will be the velocity of the man relative to the shore? There is no friction between the raft and water.

A uniform metal disc of radius R is taken and out of it a disc of diameter R is cut off from the end. The centre of mass of the remaining part will be

In the arrangement shown, co-ordinates of L-Shaped sheet are

A 50kg man is standing at one end of a 25m long boat. He starts running towards the other end. On reaching the other end his velocity is 2ms –1 relative to the boat. If the mass of the boat is 200 kg, final velocity of the boat is ( in ms –1 ), neglect friction between boat and water.

Figure shows a boy on a horizontal platform A on a smooth horizontal surface, holding a rope attached to a box B. Boy pulls the rope with a constant force of 50 N. The combined mass of platform A and boy is 250 kg and that of box B is 500 kg. The velocity of A relative to the box B 5 s after the boy on A begins to pull the rope, will be :

Two particles of masses 4 kg and 6 kg are at rest separated by 20 m. If they move towards each other under mutual force of attraction, the position of the point where they meet is

The co-ordinates of centre of mass of particles of mass 10, 20 and 30 gm are (1, 1, 1) cm.The position co-ordinates of mass 40 gm which when added to the system, the position of combined centre of mass be at (0, 0, 0) are,

One end of a thin uniform rod of length L and mass M 1 is rivetted to the centre of a uniform circular disc of radius 'r' and mass M 2 so that both are coplanar. The centre of mass of the combination from the centre of the disc is (Assume that the point of attachment is at the origin).

A ball of mass 3M rolls from rest on a smooth flat table towards another ball of mass 2M at rest with a constant velocity 5m/s. When the two balls are separated by a distance of 6m, the position of centre of mass from the mass 3M is

A uniform disc of radius R is put over another uniform disc of radius 2R of same thickness and density. The peripheries of the two discs touch each other. The position of their centre of mass is

Two balls of equal masses are thrown at the same time in vacuum. While they are in vacuum, the acceleration of their centre of mass

A bomb moving in a parabolic path explodes into two fragments of equal masses. The accelaration of the centre of mass of the fragments when both are in air is equal to

Choose the wrong statement

Particles of masses m, 2m, 3m,…… nm grams are placed on the same line at distances l, 2l, 3l, …. nl cm from a fixed point. The distance of centre of mass of the particles from the fixed point in centimetre is

The mass of a uniform ladder of length 5 m is 20 kg. A person of mass 60 kg stands on the ladder at a height of 2 m from the bottom. The position of centre of mass of the ladder and man from the bottom nearly is

A circular plate has a uniform thickness and has a diameter 56 cm. A circular disc of diameter 42 cm is removed from one edge of the plate. The distance of centre of mass of the remaining portion from the centre of the circular plate is

Two particles having masses m and 2m are travelling along x-axis on a smooth surface with velocities u 1 and u 2 , collide. If their velocities after collision are v 1 and v 2 , then the ratio of velocities of their centre of mass before and after impact is

Two particles A and B initially at rest move towards each other under a mutual force of attraction. At the instant when the speed of A is V and the speed of B is 2v, the speed of the centre of mass of the system is

A wooden log of mass 120kg is floating on still water perpendicular to the shore. A man of mass 80kg is standing at the centre of mass of the log and he is at a distance of 30m from the shore. When he walks through a distance of 10m towards the shore and halts, now his distance from the shore is

Two bodies of masses 5kg and 3kg are moving towards each other with 2ms –1 and 4ms –1 respectively. Then velocity of centre of mass is

Identify the correct statement. In the absence of external force, a) the kinetic energy associated with the motion of centre of mass is conserved b) centre of mass is not accelerated c) the centre of mass always moves in curved line d) centre of mass must be at rest

Mass of a ring is non-uniformly distributed around its geometric centre. If R is radius of the ring, then a) Centre of mass does not coincide with geometric centre b) Position of centre of mass from the geometric centre will be x (0 < x < R) c) Centre of mass will be nearer to the greater mass distribution d) Centre of mass may lie out side the periphery

Consider the following two statements. A) Linear momentum of the system remains constant. B) Centre of mass of the system remains at rest.

A boat of mass 80 kg is floating on still water. A dog of mass 20 kg on the boat is at a distance of 10m from the shore. The dog moves on the boat by a distance of 2m towards the shore. The distance of the dog from the shore is

A shell in flight explodes into n equal fragments, k of the fragments reach the ground earlier than the other fragments. The acceleration of their centre of mass subsequently will be

The density of a non-uniform rod of length 1m is given by λ(x) = p(1 + qx 2 ) where p and q are constants and 0≤x≤1. The centre of mass of the rod will be at ………..

Two blocks (from very far apart) are approaching towards each other with velocities as shown in figure. The coefficient of friction for the blocks is µ = 0.2. Initial velocity of centre of mass of the system is

Acceleration of two identical particles moving in a straight line are as shown in figure. The corresponding a-t graph of their centre of mass will be:

The 3 kg block is projected along the frictionless surface with a velocity of 2 m/s as shown in figure. What will be the velocity of 3 kg block when 6 kg block will be moving with same velocity as the centre of mass of the blocks.

Two bodies of mass 1 kg and 3 kg have position vectors i ^ + 2 j ^ + k ^ and – 3 i ^ – 2 j ^ + k ^ , respectively. The centre of mass of this system has a position vector.

A man of 50 kg mass is standing in a gravity free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed of 2 ms – 1 . When the stone reaches the floor, the distance of the man above the floor will be

Two persons of masses 55 kg and 65 kg respectively are at the opposite ends of a boat. The length of the boat is 3.0 m and weighs 100 kg. The 55 kg man walks up to the 65 kg man and sita with him. If the boat is in still water the centre of mass of the system shifts by

A body A of mass M while falling vertically downwards under gravity breaks into two parts: a body B of mass 1 3 M and body C of mass 2 3 M. The centre of mass of bodies B and C taken together shifts compared to that of body A towards:

Three masses are placed on the x-axis: 300 g at origin, 500 g at x = 40 cm and 400 g at x = 70 cm. The distance of the centre of mass from the origin is

Two particles are separated by a distance d. When the positions of the two particles are interchanged, the shift in the position of their centre of mass is d/3. If the mass of lighter particle is m, the mass of heavier particle is

The centre of mass of a system of two particles of masses m 1 and m 2 is at distance 8 cm from m 1 and at a distance 12 cm from m 2 . Then

Two particles of equal masses have velocity v 1 = 2 i ^ m/s and v 1 = 2 j ^ m / s . The first particle has an acceleration a 1 = ( 3 i ^ + 3 j ^ ) m / s 2 while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a:

The velocity of the CM of a system changes from v 1 = 4 i ⏞ m / s to v 2 = 3 j ⏞ m / s during time ∆ t = 2s. If the mass of the system is m: l0 kg, the constant force acting on the system is:

A man weighing 80 kg is standing on a trolley weighting 320 kg. The trolley is resting on frictionless horizontal rails. If the man starts walking on the trolley along the rails at speed I m/s (w.r.t to trolley) then after 4 s his displacement relative to the ground will be:

In a gravity free space, a man of mass M standing at a height h ft above the floor, throws a ball of mass m straight down with a speed u. When the ball reaches the floor, the distance of the man above the floor will be

Three balls of different masses are thrown at different instants up against gravity. While all the three balls are in air the centre of mass of the system of three balls has an acceleration:

Two blocks of masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse give a velocity of 14 m/s to the heavier block in the direction of the lighter block. The velocity of centre of mass is:

The centre of mass reference frame is also known as zero momentum frame because

Two blocks of different masses are attached to a spring and the system is kept on a smooth horizontal surface. Now if any of the blocks is given a sharp impulse, what will be the motion of centre of mass (COM) of the system with respect to ground after a long time

A carpenter has constructed a toy as shown in the figure. If the density of the material of the sphere is 12 times that of cone, the position of the centre of mass of the toy is given by:

Three particles of masses 1 kg, 2 kg, and 3 kg are located the vertices of an equilateral triangle of side a. The x, y coordinates of the centre of mass are

Centre of mass of three particles of masses I kg, 2 kg and 3 kg lies at the point (1, 2, 3) and centre of mass of another system of particles 3 kg and 2 kg lies at the point (-1, 3, -2). Where should we put a particle of mass 5 kg so that the centre of mass of entire system lies at the centre of mass of first system?

Two blocks of masses 5 kg and 2 kg are placed on a frictionless surface and connected by a spring. An external kick gives a velocity of 14 m/s to the heavier block in the direction of lighter one. The magnitudes of velocities of two blocks in the centre of mass frame after the kick are respectively:

Figure shows a cubical box that has been constructed from uniform metal plate of negligible thickness. The box is open at the top and has edge length 40 cm. The z co-ordinate of the centre of mass of the box in cm, is

A mass m is rest on an inclined plane of mass M which is further resting on a smooth horizontal plane. Now if the mass starts moving the position of C.M. of mass of system will:

When an explosive shell travelling in a parabolic path under the effect of gravity explodes in the mid air, the centre of mass of the fragments will move

The centre of mass of a non-uniform rod of length L whose mass per unit length λ varies as λ = k . x 2 L where k is a constant and x is the distance of any point on rod from its one end, is (from the same end)

A disc (of radius r cm) of uniform thickness and uniform density σ has a square hole with sides of length I = r 2 cm. One corner of the hole is located at the centre of the disc and centre of the hole lies on y-axis as shown. Then the y-coordinate of position of centre of mass of disc with hole (in cm) is

From the circular disc of radius 4R two small disc of radius R are cut off. The centre of mass of the new structure will be:

Eight solid uniform cubes of edge l are stacked together to form a single cube with centre O. One cube is removed from this system. Distance of the centre of mass of remaining 7 cubes from O is

A wire of uniform cross-section is bent in the shape shown in figure. The co-ordinate of the centre of mass of each side are shown in (figure). The coordinates of the centre of mass of the system are

A homogeneous plate PQRST is as shown in figure. The centre of mass of plate lies at midpoint A of segment QT. Then the ratio of b a is ( PQ = PT = b ; QR = RS = ST = a )

If the density of material of a square plate and a circular plate shown in is same, the centre of mass of the composite system will be

Three identical spheres each of radius R are placed touching each other on a horizontal table as shown in figure. The co-ordinates of centre of mass are:

Four particle of masses m 1 = 2 m , m 2 = 4 m , m 3 = m and m 4 are placed at four corners of a square. What should be the value of m 4 so that the centres of mass of all the four particles are exactly at the centre of the square?

The centre of mass of a system of two particles of masses m 1 and m 2 is at a distance d 1 from m 1 and at a distance d 2 from mass m 2 such that

Three particles of masses 1 kg, 3 2 kg, and 2kg are located the vertices of an equilateral triangle of side a. The x, y coordinates of the centre of mass are

Three identical particles each of mass 1 kg are placed with their centres on a straight line. Their centres are marked A, B and C respectively. The distance of centre of mass of the system from A is

For the hollow sphere shown in figure. Which of the following points is the likely position of the centre of mass of the system shown in figure :

Two particles whose masses are 30 kg and 10 kg and their position vectors are − ı ^ − ȷ ^ − k ^ and i ^ + j ^ + k ^ respectively would have the centre of mass at position :

The linear density of a thin rod of length 1 m varies as λ = 1 + 2x , where x is the distance from its one end. Distance of centre of mass of rod from this end is :

Find out coordinates of centre of mass of the system:

Two blocks of masses 10 kg and 4 kg are connected by a spring of negligible mass. Spring Constant of spring is K = 140 N/M and blocks are placed on a frictionless horizontal surface. An impulse gives a speed of 14 m/s to 10 kg block in the direction of the lighter block. Then, the maximum compression in the spring will be

A man of 50 kg is standing at one end on a boat of length 25m and mass 200 kg. If he starts running and when he reaches the other end, has a velocity 2ms -1 with respect to the boat. The final velocity of the boat is

Three masses 2 kg, 3 kg and 4 kg are lying at the corners of an equilateral triangle of side ℓ .The (X) coordinate of center of mass is

Three rods of the same mass are placed as shown in the figure. What will be the co-ordinates of the center of mass of the system ?

A uniform circular plate of radius 2R has a circular hole of radius R cut out of it. The centre of the smaller circle is at a distance of R/3 from the centre of the larger circle. What is the position of the centre of man of the plate

A boy of mass m stands on one end of a wooden plank of length I and mass M. The plank is floating on water. If the boy walks from one end of the plank to the other end at a constant speed, the resulting displacement of the plank is given by

A rod of length 3 m and its mass acting per unit length is directly proportional to distance x from one of its end, then its centre of gravity from that end will be at

Three identical particles each of mass 1 kg are placed touching each other with their centers on a straight line. their centers are marked A. B and C respectively. The distance of center of mass of the system from A is

Two particles of same mass are permitted to move towards each other along the line joining their centers of mass. At a particular moment of time their speeds are v and 2 v What is the speed of their common center of mass at this instant ?

Two blocks of masses 10 kg and 4 kg are connected by a spring of negligible mass and placed on a friction less horizontal surface. An impulse gives a velocity of 14 m/s to the heavier block in the direction of lighter block. The velocity of center of mass is

Two atoms of hydrogen are located at r 1 , and r 2 . Their center of mass is at

Four identical spheres each of radius 10 cm and mass 1 kg each are placed on a horizontal surface touching one another so that their centres are located at the corners of square of side 20 cm. What is the distance of their center of mass from center of either sphere ?

If fig four identical spheres of equal mass m are suspended by wires of equal length /, so that all spheres are almost touching to each other. If the sphere 1 is released from the horizontal position and all collisions are elastic, the velocity of sphere 4 iust after collision is

A body A of mass M while falling vertically downwards under gravity breaks into two parts; a body B of mass M/3 and body C of mass 2 M/3. The center of mass of bodies B and C taken together shifts compared to that of body A towards

A thin uniform bar lies on a frictionless horizontal surface and is free to move in any way on the surface. Its mass is 0.16kg and length is 1.7m. Two particles of each of mass 0.08 kg are moving on the same surface and towards the bar in the direction perpendicular to the bar, one with a velocity of 10 m/s and the other with velocity 6 m/s. If collision between particles and bar is completely inelastic, both particles strike with bar simultaneously. The velocity of center of mass after collision is

A bullet of mass m moving with velocity v strikes a block of mass Mat rest and gets embedded into it. The kinetic energy of the composite block will be

If the net external forces acting on the system of particles is zero, then which of the following may vary?

For which of the following does the centre of mass lie outside the body? [NCERT Exemplar]

A cracker is thrown into air with a velocity of 10 ms – 1 at an angle of 45° with the vertical. When it is at a height of (1/2) m from the ground, it explodes into a number of pieces which follow different parabolic paths. What is the velocity of centre of mass, when it is at a height of 1 m from the ground? (Take, g = 10 ms – 2 )

Two blocks ot masses 10 kg and 30 kg are placed along a vertical line. The first block is raised through a height of 7 cm. By what distance should the second mass be moved to raise the centre of mass by 1 cm?

A circular plate of diameter a is kept in contact with a square plate of edge a as shown in figure. The density of the material and the thickness are same everywhere. The centre of mass of the composite system will be

Both the blocks as shown in the given arrangement are given together a horizontal velocity towards right. If a CM be the subsequent acceleration of the centre of mass of the system of blocks, then a CM will be

In a free space, a rifle of mass M shoots a bullet of mass m at a stationary block of mass M at a distance D away from it. When the bullet has moved through a distance d towards the block, the centre of mass of the bullet-block system is at a distance of

Three identical spheres, each of mass M, are placed at the comers of a right angle triangle with the mutually perpendicular sides equal to 2 m (see figure). Taking the point of intersection of the two mutually perpendicular sides as the origin, find the position vector of centre of mass. [NEET 2020]

A particle of mass 1 kg has velocity v 1 = ( 2 t ) i ^ and another particle of mass 2 kg has velocity v 2 = ( t 2 ) j ^ . Match the following columns and mark the correct option from the codes given below. Column I Column II (A) Net force on centre of mass at 2 s (p) 20 9 unit (B) Velocity of centre of mass at 2 s (q) 68 unit (C) Displacement of centre of mass in 2s (r) 80 / 3 unit (s) None Codes A B C

A T-shaped object with dimensions as shown in the figure, is lying on a smooth floor. A force F is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect to C.

Two blocks of masses m and 2m are kept on a smooth horizontal surface. They are connected by an ideal spring of force constant k. Initially, the spring is unstretched. A constant force is applied to the heavier block in the direction as shown in figure. Suppose at time t, displacement of smaller block is x, then displacement of the heavier block at this moment would be

A uniform circular disc of radius a is taken. A circular portion of radius b has been removed from it as shown in the figure. If the centre of hole is at a distance c from the centre of the disc, the distance x 2 of the centre of mass of the remaining part from the initial centre of mass O is given by

A circular ring of mass 6 kg and radius a is placed such that its centre lies at the origin. Two particles of masses 2 kg each are placed at the intersecting points of the circle with positive X-axis and positive Y-axis. Then, the angle made by the position vector of centre of mass of entire system with X-axis is

Three bodies having masses 5 kg, 4 kg and 2 kg are moving at the speeds of 5 ms – 1 , 4 ms – 1 and 2 ms – 1 , respectively along X-axis. The magnitude of velocity of centre of mass is [AllMS 2018]

Two masses of 6 and 2 unit, are at positions ( 6 i ^ – 7 j ^ ) and ( 2 i ^ + 5 j ^ – 8 k ^ ) respectively. The coordinates of the centre of mass are [JIPMER 2017]

In the diagram shown below, m 1 and m 2 are the masses of two particles and x 1 and x 2 are their respective distances from the origin O. The centre of mass of the system is [J&K CET 2011]