Centre of Mass & Collisions

Two particles of masses 2 kg and 3 kg are located at x = 0 and x = 10 m. Find the x-coordinate of their centre of mass.

Three particles of masses 1 kg, 2 kg, and 3 kg are placed at (0,0), (2,0), and (0,3) respectively. Find the y-coordinate of their centre of mass.

Find the position of the centre of mass of a uniform rod of length 6 m, measured from one end.

A uniform disc of mass 8 kg has a smaller disc of mass 2 kg cut out from one edge, the small disc's centre being 0.3 m from the centre of the original disc. Find the distance of the centre of mass of the remaining piece from the centre of the original disc.

Two blocks of masses 4 kg and 6 kg move with velocities 3 m/s and 2 m/s respectively in the same direction. Find the velocity of their centre of mass.

Two masses 1 kg and 2 kg have accelerations 3 m/s² and 1.5 m/s² respectively, both in the same direction. Find the acceleration of their centre of mass.

A gun of mass 5 kg fires a bullet of mass 25 g with a muzzle speed of 200 m/s. Find the recoil speed of the gun.

A 6 kg bomb at rest explodes into two fragments of masses 2 kg and 4 kg. If the 2 kg fragment moves at 12 m/s, find the speed of the 4 kg fragment.

A stationary object explodes into two parts of masses m and 4m. What is the ratio of their kinetic energies, KE_m : KE_4m?

Two balls collide head-on. Before collision, ball A moves at 6 m/s and ball B at 2 m/s in the same direction. After collision, A moves at 3 m/s and B at 5 m/s. Find the coefficient of restitution.

A 3 kg ball moving at 8 m/s collides with a stationary 5 kg ball, and they stick together. Find their common velocity after collision.

A 4 kg ball moving at 10 m/s collides elastically head-on with an identical stationary 4 kg ball. Find the velocity of the first ball after collision.

A 9 kg ball moving at 6 m/s collides elastically head-on with a stationary 3 kg ball. Find the velocity of the 3 kg ball after collision.

A 1 kg ball moving at 5 m/s collides elastically head-on with a stationary 9 kg ball. Find the velocity of the 1 kg ball after collision.

A ball is dropped from a height of 4 m onto a rigid floor. If the coefficient of restitution is 0.5, find the height it reaches after the first bounce.

A ball is dropped from a height of 5 m (g = 10 m/s²) and bounces off the ground with coefficient of restitution e = 0.6. Find its speed immediately after the second bounce.

A ball collides obliquely and elastically with an identical stationary ball. If the first ball moves off at 30° to its original direction, at what angle does the second ball move off (on the other side)?

A force acts on a 2 kg object initially at rest, changing its momentum to 10 kg·m/s in 0.5 s. Find the magnitude of the average force.