Two particles of masses `m_1 and m_2` move on the same plane. If their relative velocity is u, and the velocity of their centre of mass is v, show that the total kinetic energy is
`1/2(m_1+m_2)v^2+1/2 ((m_1m_2)/(m_1+m_2))u^2`.

Find the velocity of the centre of mass of two identical particles moving with velocities v_(1) and v_(2) .

Two particles of masses 1 kg and 2 kg are positioned on x-and y-axes at distances of 1 m and 2 m from the origin respectively. Find the position of the centre of mass of the system.

Two particle of mass m_1 and m_2 approach each other due to their mutual gravitational attraction only. Then

Two particles of masses m and 2m with charges 2q and 2q are placed in a uniform electric field E and allowed to move for the same time. The ratio of their kinetic energies will be

Two particles have masses m & 4m and their kinetic energies are in the ratio 2: 1 . What is the ratio of their linear momenta?

Two bodies of masses m_(1) and m_(2) are separated by a distance R. The distance of the centre of mass of the bodies from the mass m_(1) is

Two particles of masses m_1 and m_2 are kept at a separation of d. when a third particle is kept at a distance of d/3 from m_1 , then it does not experience any net force. Determine the ratio (m_2)/(m_1) .

A boy of mass m_1 , standing on a smooth horizontal surface, throws a sphere of mass m_2 parallel to the surface. After a time t, if the separation between them becomes x, then show that the work done by the boy in throwing the sphere =1/2 (x/t)^2((m_1m_2)/(m_1+m_2))