A particle of mass m is tied to one end of a light string and the other end of the string passes through a small hole at the centre of the table as shown. The particle is rotating along a circle of radius R on the smooth table with speed $$V0$$. Now the free end of the string is slowly pulled downward by a distance $$R/2$$. Then the final tension in the string is

Question

A particle of mass m is tied to one end of a light string and the other end of the string passes through a small hole at the centre of the table as shown. The particle is rotating along a circle of radius R on the smooth table with speed $$V0$$. Now the free end of the string is slowly pulled downward by a distance $$R/2$$. Then the final tension in the string is

Infinity Learn · Accepted Answer

No external torque is acting on the particle about the axis of rotation.Conserving angular momentum, mv.$$R2=mv0R$$⇒$$v=2v0$$∴Final tension, $$T=m$$.$$v2R/2=m$$.$$(2v0)2R/2$$⇒$$T=8mv02R$$

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