Question

A mass m is attached to a string of length r and is swung in a vertical circle. The mass is released from the top of the circle. The study focuses on the forces acting on the mass and the concepts of centripetal force, tension, and energy transformations.

For a particle rotating in a vertical circle with uniform speed, the maximum and minimum tension in the string are in the ratio 5: 3. If the radius of vertical circle is 2m, then find the speed of revolving body.

(a) The bob of a pendulum is released from a horizontal position. If the length of the pendulum is L, what is the speed with which it arrives at the lower most point, given that it dissipates its 10 % energy against air resistance? (b) If the same bob is releases as shown in the figure, find the speed at the lowermost point if it dissipates no energy.

A body tied to one end of a string is made to revolve in a vertical plane. Derive the expression for the velocity of the body and tension in the string at any point. Hence find (i) tension at the bottom and top of the circle. (ii) Minimum velocity at the lowest point so that it is just able to loop the vertical loop and (c) the minimum velocity at the top.