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

Which of the following statements are correct ?

(1)   Centre of mass of a body always coincides with the centre of gravity of the body.

(2)   Centre of mass of a body is the point at which the total gravitational torque on the body is zero.

(3)   A couple on a body produces both translational and rotational motion in a body

(4)   Mechanical advantage greater than one means that small effort can be used to lift a large load.

Two identical balls A and B having velocities of 0.5 m s^$$-$$1 and $$-$$0.3 m s^$$-$$1 respectively collide elastically in one dimension. The velocities of B and A after the collision respectively will be :

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