A ball suspended by a thread swings in a vertical plane so that its acceleration in the extreme position and lowest position are equal. The angle  of thread deflection in the extreme position will be - 2

Options

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

Answer

D

Explanation

`g sintheta=(v^(2))/(R)=(2gh)/(R)=(2gR(1-costheta))/(R)`
or `sintheta=2(1-costheta)`
`2sin.(theta)/(2)cos.(theta)/(2)=2(2sin^(2).(theta)/(2))`
`rArr" "tan.(theta)/(2)=(1)/(2)rArr(theta)/(2)=tan^(-1)((1)/(2)) or theta=2tan^(-1)((1)/(2))`

Note In extreme position of pendulum, only tangential componet of acceleration `(a_(t)=gsintheta)` is present. In lowest position, only normal acceleration `(a_(n)=v^(2)//R)` is present.