Question

A small smooth ring of mass m is threaded on a light inextensible string of length 8L which has its ends fixed at points in the same vertical line at distance 4L apart. The ring describes horizontal circles at constant speed with both parts of the string taut and with the lower portion of the string horizontal. Find the speed of the ring and tension in the string. The ring is then tied at the midpoint of the string and made to perform horizontal circles at constant speed of 3√gL . Find the tension in each part of the string.

Answer 1

Apply Newton’s second law in the radial direction in each case. 

When the string passes through the ring, the tension in the string is the same in both the parts. Also from geometry,