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

Options

A. mg
B. 3mg
C. 4 mg
D. 6 mg

Answer

B

Explanation

From energy conservation

`1/2 mV_(A)^(2)=1/2 mV_(B)^(3)+mgR`
`V_(A)^(2)-V_(B)^(2)=2 gR`
`T_(A)-mg=(mV_(A)^(2))/R`
`T_(B)=(mV_(B)^(2))/R`
`T_(A)-T_(B)=mg +m/R (V_(A)^(2)-V_(B)^(2))=mg+m/R. 2gR= 3mg`