A uniform steel rod of mass m and length l is pivoted . If it is inclienn with the horizontal at an angle `theta` its potential energy will be

Options

A. `(1)/(2)mglcostheta`
B. `(1)/(2)mglsintheta`
C. `mglcostheta`
D. `mglsintheta`

Answer

B

Explanation

The weight of the rod acts at the centre of gravity which is at a distance of l/2 from the pivoted. End. When the rod makes an angle `theta` with the horizontal, the vertical height of the centre of gravity is
`h = (l)/(2) sin theta`
i.e., the centre of gravity rises by an amount h. Therefore,
PE = mgh `= (1)/(2) mgl sin theta`,