Q. 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) $m_{1} + m_{2}(a + b)$
B) $\left\lbrack \frac{m_{1}m_{2}}{2}a + m_{2}\frac{b}{2} \right\rbrack$
C) $\left\lbrack \left( \frac{m_{1}}{2} + m_{2} \right)a + m_{2}\frac{b}{2} \right\rbrack$
D) $\left( \frac{m_{1}}{2} + m_{2} \right)a + m_{1}\frac{b}{2}$
Explanation
(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
$= m_{1}g\frac{a}{2} + m_{2}g\left( a + \frac{b}{2} \right) = \left\lbrack \frac{m_{1}}{2} + m_{2} \right\rbrack ga + m_{2}g\frac{b}{2}$
$= \left\lbrack \left( \frac{m_{1}}{2} + m_{2} \right)a + m_{2}\frac{b}{2} \right\rbrack g$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.