Two plates `1` and `2` move with velocities `-v ` and `2v` respectively. If the sphere does not slide relative to the plates, assuming the masses of each body as `m`, find the kinetic energy of the system (plates+sphere).

Two bodies of equal masses move with uniform velocities v and 3v respectively. Find the ratio of their kinetic energies.

Two particles having masses m_(1) and m_(2) are moving with velocities vec(V)_(1) and vec(V)_(2) respectively. vec(V)_(0) is velocity of centre of mass of the system. (a) Prove that the kinetic energy of the system in a reference frame attached to the centre of mass of the system is KE_(cm) = (1)/(2)mu V_(rel)^(2) . Where mu=(m_(1)m_(2))/(m_(1)+m_(2)) and V_(rel) is the relative speed of the two particles. (b) Prove that the kinetic energy of the system in ground frame is given by KE=KE_(cm)+(1)/(2)(m_(1)+m_(2))V_(0)^(2) (c) If the two particles collide head on find the minimum kinetic energy that the system has during collision.

Two bodies of masses m_1 and m_2 are moving with velocity v_1 and v_2 respectively in the same direction. The total momentum of the system in the frame of reference attached to the centre of mass is ( v is relative velocity between the masses)

Two bodies of masses m_(1) and m_(2) are moving with velocity v_(1) and v_(2) respectively in the same direction. The total momentum of the system in the frame of reference attached to the centre of mass I (v is relative velocity between the masses)

Two particles of mass 2m and m moving with speed v and 2v respectively perpendicular to each other collides perfectly inelastically, then Loss in kinetic energy of the system

A particle of mass m moving with velocity 2v collides with another particle of mass 3m moving with velocity v in the same direction.If it is perfect inelastic collision,the loss of kinetic energy of the system is

Two masses, m_(1) and m_(2) , are moving with velocities v_(1) and v_(2) . Find their total kinetic energy in the reference frame of centre of mass.

Two masses, m_(1) and m_(2) , are moving with velocities v_(1) and v_(2) . Find their total kinetic energy in the reference frame of centre of mass.

Two objects having same mass 'm' are moving with velocities v and 2v. Find ratio of their kinetic energies.