Question

A rectangular plank of mass $m_{1}$ and height $a$ is kept on a horizontal surface. Another rectangular plank of mass $m_{2}$ and height $b$ is placed over the first plank. The gravitational potential energy of the system is

• A. $\left[m_{1}+m_{2}(a+b)\right] g$
• B. $\left[\left(\frac{m_{1}+m_{2}}{2} a+m_{2} \frac{b}{2}\right)\right] g$
• C. $\left[\left(\frac{m_{1}}{2}+m_{2}\right) a+m_{2} \frac{b}{2}\right] g$
• D. $\left[\left(\frac{m_{1}}{2}+m_{2}\right) a+m_{1} \frac{b}{2}\right] g$

Answer 1

Answer: (C)

Height of $CG$ of mass $m_{1}=\frac{ a }{2}$
Height of $CG$ of mass $m_{2}=a+\frac{b}{2}$
$\therefore $ Gravitational potential energy of system
$=m_{1} g \frac{a}{2}+m_{2} g\left(a+\frac{b}{2}\right)$
$=\left[\frac{m_{1}}{2}+m_{2}\right] g a+m_{2} g \frac{b}{2}$
$=\left[\left(\frac{m_{1}}{2}+m_{2}\right) a+m_{2} \frac{b}{2}\right] g$