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CGP EDU Academic Team
Published on: September 12, 2026
A mass M is split into two parts, m and (M–m), which are then separated by a certain distance. What ratio of m/M maximizes the gravitational force between the two parts
Text Solution
Verified by ExpertsThe correct answer is:
B
$F = \frac{G m (M - m)}{r^2}$
For maximum force $\frac{dF}{dm} = 0$
⇒ ⇒ $\frac{d}{dm}\left(\frac{GmM}{r^{2}}-\frac{Gm^{2}}{r^{2}}\right)=0$
⇒ ⇒ $M - 2m = 0 \Rightarrow \frac{m}{M} = \frac{1}{2}$
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