Elastic and inelastic collisions in one and two dimensions

Two bodies A and B of same mass undergo completely inelastic one dimensional collision. The body A moves with velocity \(v_1\) while body B is at rest before collision. The velocity of the system after collision is \(v_2\). The ratio \(v_1 : v_2\) is :

Body A of mass 4m moving with speed \(u\) collides with another body B of mass 2m, at rest. The collision is head on and elastic in nature. After the collision the fraction of energy lost by the colliding body A is :

A moving block having mass m, collides with another stationary block having mass 4m. The lighter block comes to rest after collision. When the initial velocity of the lighter block is v, then the value of coefficient of restitution (e) will be

A bullet of mass 10 g moving horizontally with a velocity of 400 m s\(^{-1}\) strikes a wooden block of mass 2 kg which is suspended by a light inextensible string of length 5 m. As a result, the centre of gravity of the block is found to rise a vertical distance of 10 cm. The speed of the bullet after it emerges out horizontally from the block will be

Two identical balls \(A\) and \(B\) having velocities of 0.5 m/s and -0.3 m/s respectively collide elastically in one dimension. The velocities of \(B\) and \(A\) after the collision respectively will be