The maximum tension in the string of a simple pendulum is 1.2 times the minimum tenstion. If `0_(0)` is the angular amplitude, then `0_(0)` is

Options

A. `cos^(-1)((4)/(5))`
B. `cos^(-1)((3)/(4))`
C. `cos^(-1)((15)/(16))`
D. `cos^(-1)((7)/(8))`

Answer

D

Explanation

`T_(1)-mg=(mv^(2))/(l)`
`T_(1)=mg+(m)/(l)[2gl(1-cos'theta)]`
`T_(1)=3mg-2mg cos theta`
`T_(2)=mg cos theta`
`T_(2)=mg cos theta`
`(T_(1))/(T_(2))=(6)/(5)`
`(3mg-2mgcostheta)/(mgcostheta)=(6)/(5)`
`15 mg-10 mg cos theta=6 mg cos theta`
`15 mg= 16 mg cos theta`
`cos theta =15//16`