Question

A uniform rod of mass $5\text{kg}$ and length $3\text{m}$ is held at an angle $\theta ={37}^{\circ }$ with the horizontal as shown in the figure. The potential energy of the rod is (in $\text{J}$)

• A. $\frac{21g}{2}$
• B. $\frac{9g}{2}$
• C. $12g$
• D. $6g$

Answer 1

The correct option is B $\frac{9g}{2}$


For uniform linear body
Potential energy, $U=mgh$
where $m=5\text{kg}$
$h=$ distance of centre of mass from ground $=\frac{l}{2}\sin \theta =\frac{3}{2}\sin \theta$
$=\frac{3\sin \theta }{2}$

$U=\frac{3mg\sin \theta }{2},$ where $m=5\text{kg}$, $\theta ={37}^{\circ }$
$\Rightarrow U=\frac{9g}{2}\text{J}$