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.

A rigid ball of mass m strikes a rigid wall at 60^o and gets reflected without loss of speed as shown in the figure. The value of impulse imparted by the wall on the ball will be :

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