Q. The gravitational force between a point like mass $M$ and an infinitely long, thing rod of linear mass density perpendicular to distance $L$ from $M$ is
A) $\frac{MG\lambda}{L}$
B) $\frac{1}{2}\ \frac{MG\lambda}{L}$
C) $\frac{2MG\lambda}{L^{2}}$
D) Infinite
Explanation
(c) [image:8_image60.emf]
Let the mass $M$ be placed symmetrically
$\Rightarrow \ F_{net} = \int_{- \infty}^{\infty}{dF\sin{\theta =}}\int_{- \infty}^{\infty}{\frac{GM(\lambda dx)}{X^{2} + L^{2}}\frac{L}{\sqrt{X^{2} + L^{2}}}}$
$\Rightarrow \ F_{net} = GM\lambda L\int_{- \infty}^{\infty}\frac{dx}{\left( X^{2} + L^{2} \right)^{3/2}}$
$\Rightarrow \ F_{net} = \frac{GM\lambda L}{L^{2}}(2)$
$\Rightarrow \ F_{net} = \frac{2GM\lambda}{L^{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.