Test Preparation on Physics-Circular motion-2

A table with a smooth horizontal surface is turning at an angular speed about its axis. A groove is made on the surface along a radius and a particle is gently placed inside the

groove at a distance from the center. the velocity of the particle for the table as its distance from the center becomes L is ` B The velocity of the particle for a stationary observer as its distance from the center becomes b is 

A hollow sphere of radius R is kept on the ground. A particle is released from rest inside the sphere at an extreme end of the horizontal diameter. At an instant, if the kinetic energy of the particle is K, find the force exerted by the particle on the surface at this instant (assume there is no friction between sphere& particle) is

The maximum and minimum tensions in a string of length 10cm with a stone 5gm tied to it and whirled in a vertical circle are in the ratio 13: 1.The velocity of the body at highest point is (total energy is constant)

A smooth hollow cone whose vertical angle is 2?, with it axis vertical and vertex downwards, revolves about its axis n times per second.Find where a particle may be placed on the inner surface of cone so that it rotates with same speed