Question

A rod of mass $M$, hinged at $O$ is kept in equilibrium with a spring of stiffness $k$ as shown. The potential energy stored in the spring is:

• A. $\frac{(mg{)}^2}{4k}$
• B. $\frac{(mg{)}^2}{2k}$
• C. $\frac{(mg{)}^2}{8k}$
• D. $\frac{(mg{)}^2}{k}$

Answer 1

The correct option is C $\frac{(mg{)}^2}{8k}$

As the rod is in equilibrium

$\therefore \sum$ Moment about O $=0$

$F_{spring}.r_{spring}=F_{gravity}.r_{gravity}$
$\therefore \left(kx\right)l=mg\frac{l}{2}$

or $x=\frac{mg}{2k}$

$U=\frac{1}{2}{kx}^2=\frac{(mg{)}^2}{8k}$