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an object of mass M is divided into two parts , which are placed at distance d. if gravitational force of attraction is max between parts, then find the ratio of mass of both parts.
Pls explain the answer.
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Explanation:
The gravitational force of attraction is, F = Gm (M - m)/d2
Differentiating w.r.t m,
dF/dm = G/d2 (M - 2m) ; d2F/dm2 < 0
When Force of attraction (F) is maximum between parts,
G/d2 (M - 2m) = 0
=> M = 2m
=> m = M/2
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