Find the increment of the kinetic energy of the closed system comprising two spheres of masses `m_1` and `m_2` due to their perfectly inelastic collision, if the initial velocities of the sphere were equal to `v_1` and `v_2`.

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

Statement-1 : In a perfectly inelastic collision between two spheres, velocity of both spheres just after the collision are not always equal. Statement-2 : For two spheres undergoing collision, component of velocities of both spheres along line of impact just after the collision will be equal if the collision is perfectly inelastic. The component of velocity of each sphere perpendicular to line of impact remains unchanged due to the impact.

A sphere P of mass m and velocity v_i undergoes an oblique and perfectly elastic collision with an identical sphere Q initially at rest. The angle theta between the velocities of the spheres after the collision shall be

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

A sphere of mass m moving with velocity v collides head -on on another sphere of same mass which is at rest. The ratio of final velocity of second sphere to the initial velocity of the first sphere is (where, e is coefficient of restitution and collision is inelastic)

A system consists of two small spheres of masses m_1 and m_2 interconnected by a weightless spring. At the moment t=0 the spheres are set in motion with the initial velocities v_1 and v_2 after which the system starts moving in the Earth's uniform gravitational field. Neglecting the air drag, find the time dependence of the total momentum of this system in the process of motion and of the radius vector of its centre of inertia relative to the initial position of the centre.

A smooth sphere of mass M moving with velocity u directly collides elastically with another sphere of mass m at rest. After collision their final velocities are V and v respectively. The value of v is