A particle of mass M is situated at the centre of a spherical shell of same mass and radius a. The magnitude of the gravitational potential at a point sutuated at a/2 distance from the centre, will be :

A mass m moving horizontally (along the x-axis) with velocity $$v$$ collides and sticks to a mass of 3m moving vertically upwards (along the y-axis) with velocity 2$$v$$. The final velocity of the combination is

A small mass attached to a string rotates on a frictionless table top as shown. If the tension in the string is increased by pulling the string causing the radius of the circular motion to decrease by a factor of 2, the kinetic energy of the mass will

A conveyor belt is moving at a constant speed of 2 ms^$$-$$1. A box is gently dropped on it. The coefficient of friction between them is $$\mu $$ = 0.5. The distance that the box will move relativce to belt before coming to rest on it, taking g = 10 m s^$$-$$2,, is