Question

A small 0.441-kg object moves on a frictionless horizontal table in a circular path of radius 2.26 m, see image below. The angular speed is 7.09 rad/s. The object is attached to a string of negligible mass that passes through a small hole in the table at the center of the circle. Someone under the table begins to pull the string downward to make the circle smaller. If the string will tolerate a tension of no more than 1350 N, what is the radius of the smallest possible circle on which the object can move? Answer to 3 significant figure

Answer 1

Since string passes through the centre of circle so torque of Tension force about the centre is zero. Hence about the centre angular momentum remains constant.

Angular momentum is given by ,

= 0.441×2.26²× 7.09

= 15.97 kg.m²/s

Tension in the string will provide the required centripetal force , so

Putting maximum value of T will give minimum value of r

r³ = 0.428

r = 0.754 m