A ball suspended by a thread swings ia a vertical plane so that its acceleration in the extreme position and lowest position are equal. The angle `theta` of thread deflection in the extreme position will be

Options

A. `tan^(-1)(2)`
B. `tan^(-1)(sqrt2)`
C. `tan^(-1)(1/2)`
D. `2tan^(-1)(1/2)`

Answer

D

Explanation

`g sin theta(v^2)/(R)=(2gh)/(R)=(2gR(1-costheta))/(R)`
`or sin theta=2(1-costheta)or2sin""(theta)/(2)cos ""(theta)/(2)=2(2sin^2""theta/2)`
`therefore tan ""(theta)/(2) = (1)/(2) or (theta)/(2) = tan^(-1) ((1)/(2))`
`implies theta = 2 tan^(-1) ((1)/(2))`