Question
A 10kg mass is to be divided into two parts, such that the force of attraction between them is maximum. What is the mass of each portion?
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Answer
Let m kg and (10 - m) kg be the mass of two parts separated by a distance r. The force is $\text{F}=\frac{\text{Gm}(10-\text{m})}{\text{r}^2}$ For force to be maximum, $\frac{\text{dF}}{\text{dm}}=0$ $\therefore\frac{\text{G}}{\text{r}^2}[\text{m}(-1)+(10-\text{m}\times1)=0]$ $\therefore\text{m}=10-\text{m}$ $\therefore\text{m}=5\text{kg}$
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