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Question

A mass M is split into two parts m and (Mm), which are, then separated by a certain distance. The ratio m/M which maximizes the gravitational force between the parts is
  1. 1:3
  2. 1:1
  3. 1:2
  4. 1:4

A
1:2
B
1:4
C
1:3
D
1:1
Solution
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The correct option is C 1:2
Gravitational force between two parts F=Gm(Mm)r2
For maxima, dFdm=0
Or ddm.Gm(Mm)r2=0
Or ddm(mMm2)=0
Or M2m=0 m=M2
Hence force between them is maximum when m:M=1:2

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