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Question

A mass M is broken into two parts of masses $$m_1$$ and $$m_2$$. How are $$m_1$$ and $$m_2$$ related so that force of gravitational attraction between the two parts is maximum?


Solution

Let mass of one part be $$x$$ 
then  $$F=\cfrac { Gx(M-x) }{ { r }^{ 2 } } \\ { F }^{ ' }=\cfrac { G }{ { R }^{ 2 } } (M-2x)\\ \Rightarrow M-2m=0$$
$$ x=\cfrac { M }{ 2 } $$ is point of maxima.

Physics

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