Question

A ball of mass m is fastened to a string. The ball swings at constant speed in a vertical circle of radius R with the other end of the string held fixed. Neglecting air resistance, what is the difference between the string's tension at the bottom of the circle and at the top of the circle? 

(A) 1·mg 

(B) 2·mg 

(C) 4·mg 

(D) 6·mg 

(E) 8·mg 

Answer 1

Correct option (B) 2·mg

At the top of the circle, ΣF = F_T + mg = mv²/R, giving F_T = mv²/R – mg. At the bottom of the circle, ΣF = F_T – mg = mv²/R, giving F_T = mv²/R + mg The difference is (mv²/R + mg) – (mv²/R – mg)