Q. The potential energy of gravitational interaction of a point mass $m$ and a thin uniform rod of mass $M$ and length $l$, if they are located along a straight line at distance $a$ from each other is
A) $U = \frac{GMm}{a}\log_{e}\left( \frac{a + l}{a} \right)$
B) $U = GMm\ \left( \frac{1}{a} - \frac{1}{a + l} \right)$
C) $U = - \frac{GMm}{l}\log_{e}\left( \frac{a + l}{a} \right)$
D) $U = - \frac{GMm}{a}$
Explanation
(c) [image:8_image61.emf]
$\Rightarrow \ dU = \frac{Gm\left( \frac{M}{l}dx \right)}{x}$
$\Rightarrow \ U\int_{}^{}{dU = \frac{GmM}{l}\ \int_{a}^{a + l}\frac{dx}{x}}$
$\Rightarrow \ U = - \frac{GmM}{l}\log_{e}\left( \frac{a + l}{a} \right)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.