The acceleration due to gravity at a height at a height 1 km above the rearth is the same as at a depth d below the surface of earth. Then

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 astronauts are floating in gravitational free space after having lost contact with their spaceship. The two will

A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm. What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N?