A simple pendulum oscillates with an anglular amplitude of `theta`. If the maximum tension in the string is 3 times the minimum tension, then the value of `cos theta` is

Options

A. `(1)/(2)`
B. `(2)/(3)`
C. `(3)/(4)`
D. `(3)/(5)`

Answer

D

Explanation

Maximum tension is at O and minimum tension is at A.
By the principle of conservation at energy
K.E. at O=P.E. at A
`therefore (1)/(2)mv^(2)=mgh =mgl (1-"cos" theta)`
`therefore v^(2)=2gl (1-"cos" theta)`

`T_("max")=mg +(mv^(2))/(l)`
`=mg +(m)/(l)[2gl (1-"cos" theta)]`
`=3 mg -2 mg "cos" theta`
and `T_("min")=mg "cos" theta`
`because T_("max")=3 T_("min ")`
`therefore 3 mg -2mg "cos" theta =3 mg "cos" theta `
`therefore 3=5 "cos" theta therefore "cos" theta =(3)/(5)`