Q. Mass $M$ is divided into two parts $xM$ and $(1 - x)M$. For a given separation, the value of $x$ for which the gravitational attraction between the two pieces becomes maximum is
A) $\frac{1}{2}$
B) $\frac{3}{5}$
C) 1
D) 2
Explanation
(a) $F \propto xm \times (1 - x)m = xm^{2}(1 - x)$
For maximum force $\frac{dF}{dx} = 0$
$\Rightarrow \frac{dF}{dx} = m^{2} - 2xm^{2} = 0$
$\Rightarrow x = 1/2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.