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physics

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A mass M is split into two parts, m and M - m, which are then separated by a certain distance. What ratio m/M maximizes the magnitude of the gravitational force between the parts?

  • physics -

    F = G m (M -m)/r^2
    maximize
    m(M-m) where M is a constant total mass
    y = m(M-m) = M m - m^2
    dy/dm = M - 2 m
    that = 0 when
    M = 2 m
    m = M/2
    so split it in two

  • physics -

    2m

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