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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

A
1:4
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B
1:3
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C
1:2
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D
1:1
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Solution

The correct option is C 1:2

The two parts of masses are m and (Mm).

The gravitational force between the parts is given as,

F=Gm(Mm)r2

The condition for maximum force is given as,

dFdm=0

ddm(Gm(Mm)r2)=0

Gr2(M2m)=0

(M2m)=0

mM=12

Thus, the ratio mM is 12.


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