A simple pendulum swings with angular amplitude `theta`. The tension in the string when it is vertical is twice the tension in its extreme position. Then, ` cos theta` is equal to

Options

A. `1//3`
B. `1//2`
C. `2//3`
D. `3//4`\

Answer

4

Explanation

`T-mg cos theta=(mv^(2))/R=0`
(v=0 at extreme position)
`T= mg cos theta.....(i)`
At mean position
`2T-mg=mv^(2).....(2)`
alos, `v=sqrt(2g(R-Rcos theta)).....(3)`
from (2) and (3)
`2T-mg =m/R 2gR(1-cos theta)`

`T=3/2 mg -mg cos theta.....(4)`
from (1) and (4)
`2mg cos theta=(3mg).2`
`cos theta=3/4`