First slide

Gravitational force and laws

Question

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

Difficult

A

1/3
B

1/2
C

1/4
D

1/5

Solution

$F = \frac{Gm (M - m)}{r^{2}}$
For maximum force $\frac{dF}{dm} = 0$
$\begin{array}{l} \Rightarrow \frac{d}{dm} (\frac{GmM}{r^{2}} - \frac{{Gm}^{2}}{r^{2}}) = 0 \\ \Rightarrow M - 2 m = 0 \Rightarrow \frac{m}{M} = \frac{1}{2} \end{array}$

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