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
$=m_{1}g\frac{a}{2}+m_{2}g\left(a+\frac{b}{2}\right)$
$=\left[\frac{m_1}{2}+m_2\right]ga+m_{2}g\frac{b}{2}$
$=\left[\left(\frac{m_1}{2}+m_2\right)a+m_2\frac{b}{2}\right]g$