question_answer

A rod of mass m and length (is made to stand at an angle of \[60{}^\circ \] with the vertical. Potential energy of the rod in this position is

A) \[mg\,\ell \]

B) \[\frac{mg\,\ell }{2}\]

C) \[\frac{mg\,\ell }{3}\] 

D) \[\frac{mg\,\ell }{4}\]

Correct Answer: D

Solution :

[d] For any uniform rod, the mass is supposed to be concentrated at its centre. \[\therefore \]  height of the mass from ground is \[h=\left( 1/2 \right)\sin {{30}^{\operatorname{o}}}\] \[\therefore \]  Potential energy of the rod \[=m\times g\times \frac{\ell }{2}\sin {{30}^{\operatorname{o}}}\] \[=m\times g\times \frac{\ell }{2}\times \frac{1}{2}=\frac{mg\ell }{4}\]