A mass M is split into two parts m and (M−m), which are, then separated by a certain distance. The ratio m/M which maximizes the gravitational force between the parts is
1:3
1:1
1:2
1:4
A
1:2
B
1:4
C
1:3
D
1:1
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Solution
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The correct option is C1:2 Gravitational force between two parts F=Gm(M−m)r2
For maxima, dFdm=0
Or ddm.Gm(M−m)r2=0
Or ddm(mM−m2)=0
Or M−2m=0⟹m=M2
Hence force between them is maximum when m:M=1:2
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