Test: Centre Of Mass (Competition Level) - JEE MCQ

Particles of masses 1 kg and 3 kg are at m  then instantaneous position of their centre of mass is  

A uniform metre rod is bent into L shape with the bent arms at 90^o to each other. The distance of the centre of mass from the bent point is  

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

Two identical thin uniform rods of length L each are joined to form T shape as shown in the figure. The distance of centre of mass from D is  

Two particles of equal masses have velocities    First particle has an acceleration    while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a path of  

Two bodies of masses m₁ and m₂ are moving with velocity v₁ and v₂ respectively in the same direction. The total momentum of the system in the frame of reference attached the centre of mass is (v is relative velocity between the masses) 

A body of mass m moving at a constant velocity v hits another body of the same mass moving with a velocity v/2 but in the opposite direction and sticks to it. The common velocity after collision is 

A body of mass 5 kg is acted on by a net force F which varies with time t as shown in graph, then the net momentum in SI units gained by the body at the end of 10 seconds is

A force time graph for the motion of a body is as shown in figure. Change in linear momentum between 0 and 6 s is 

A ball of mass 10 g hits a hard surface vertically with a speed of 5 m/s and rebounds with the same speed. The ball remains in contact with the surface for 0.01 s. The average force exerted by the surface on the ball is  

Locate the centre of mass of a uniform semicircular ring (or wire) of radius R and linear mass density λ.

The linear momentum of a particle varies with time t as p = a + bt + ct². Which of the following statement is correct?  

A block Q of mass M is placed on a horizontal frictionless surface AB and a body P of mass m is released on its frictionless slope. As P slides by a length L on this slope of inclination θ, the block Q would slide by a distance

A bomb of mass 12 kg, initially at rest explodes into two pieces of masses 4 kg and 8 kg. The speed of the 8 kg mass is 6 m/s. The kinetic energy of the 4 kg mass is  

A pulley fixed to the ceiling carries a string with blocks of mass m and 3 m attached to its ends. The masses of string and pulley are negligible. When the system is released, its centre of mass moves with what acceleration?

A 1 kg ball moving at 12 m/s collides head-on with a 2 kg ball moving in the opposite direction at 24 m/s. If the coefficient of restitution is 2/3 then the final speeds of the two balls are respectively  

Two spheres A and B of masses m and 2m and radii 2R and R respectively are placed in contact as shown. The COM of the system lies

Ball 1 collides with another identical ball 2 at rest as shown in figure. For what value of coefficient of restitution e, the velocity of second ball becomes two times that of 1 after collision

There are some passengers inside a stationary railway compartment. The centre of mass of the compartment itself (without the passengers) is C₁, while the centre of mass of the 'compartment plus passengers' system is C₂. If the passengers move about inside the compartment then

“A truck of mass 15 tons moving with one meter per second collides with the stationary truck of 10 tons and they start to move together.
In the above question, the energy lost in the collision is”

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

A particle of mass 1 g moving with a velocity  m/s experiences a perfectly inelastic collision with another particle of mass 2 g and moving with velocity  m/s. The velocity of the combined particle is  

With O as the origin of the coordinate axis, the X and Y-coordinates of the centre of mass of the system of particles shown in the figure may be given as? (Here m and 2m represent the masses of the particles)

A batsman deflects a ball at an angle 90^o without changing its initial speed which is equal to 54 km/h. The impulse imparted to the ball whose mass is 0.5 kg is  

Four particles of masses m₁, m₂, m₃ and m₄ are placed at the vertices A,B C and D as respectively of a square shown. The COM of the system will lie at diagonal AC if

A ball moving with a constant speed hits another identical ball at rest. If co-efficient of restitution equals (2/3) then the ratio of speeds of the second ball to that of the first ball after collision will be  

The centre of mass of three bodies each of mass 1 kg located at the points (0,0),(3,0) and (0,4) in the XY plane is