A simple pendulum of length l has a maximum angular displacement `theta`. The maximum kinetic energy of the bob of mass m will be

Options

A. `mgl (1 + "cos" theta)`
B. `mg (1 + "cos"^(2) theta)`
C. `mgl (1 - "cos" theta)`
D. `mgl ("cos" theta- 1)`

Answer

C

Explanation

When the bob is at the mean (equilibrium) position it has maximum K.E. and at the extreme, (maximum `theta)`, it has maximum P.E.

`(K.E.)_("max")=(P.E.)_("max")=mgh`
`=mg [l-l "cos" theta]=mg l (1- "cos" theta)`