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A mass M is broken into two parts, m & (...

A mass M is broken into two parts, m & (M-m). How is m related to M so that the gravitational force between two parts is maximum?

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Let `m_(1) = m , m_(2) = M-m`
`F = (G(M-m).m)/(r^2) = (G(Mm - m^2))/(r^2)`
Differenentiating with respect to m,
`(dF)/(dm) = G/(r^2) (M - 2m)`
For F is maximum `(dF)/(dm) = 0`
`G/(r^2) (M - 2m) = 0`
`M = 2m implies m = M/2`
`m_(1) = m_(2) = M/2`.
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