A rod of mass m and length l is made to stand at an angle of `60^@` with the vertical. Potential energy of the rod in this position is

Options

A. a)mgl
B. b)`(mgl)/2`
C. c)`(mgl)/3`
D. d)`(mgl)/4`

Answer

D

Explanation

Centre of the mass of the rod lies at the midpoint and when the rod is displaced through an angle `60^@` it rises to point AB.
From the figure
`sin 30^@= (BC)/(AB)`
or `sin 30^@=L/(l//2)`
`or 1/2=L/(l//2)`
or `L=l/4`
The potential energy of the rod in this position is
`U=mg L`
`U=mg l/4`