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+costheta)`
B. `mgl(1+cos^2theta)`
C. `mgl(1-costheta)`
D. `mgl(costheta-1)`

Answer

C

Explanation

According to question, when bob is at rest, the pendulum has only potential energy
(PE) = mgl
When bob displaced by smaller angular displacement 0, the pendulum loses PE of bob and it gets converted into kinetic energy (KE). So, from conservation of energy Loss in PE = gain in KE
`therefore KE = mgl - mgi costheta = mgl (1- cos theta)`