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Question

Two masses M and 4M are separated by a distance d. What will be the distance of mass 1 kg from M and 4M respectively, so that net gravitational force on it is zero?

A

d2,d2
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B

d3,2d3
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C

2d3,d3
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D

d4,3d4
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Solution

The correct option is B
d3,2d3
Let mass 1 kg be placed at a distance x from mass M as shown in the figure.




Gravitational force on mass 1 kg due to mass 4M:

F=G(4M).(1)(dx)2=4GM(dx)2...(i)
Gravitational force on mass 1 kg due to mass M:

F=GM(1)x2=GMx2...(ii)
For net gravitational force to be equal to zero, FF=04GM(dx)2GMx2=04GM(dx)2=GMx2(dx)2=4x2dx=2xx=d3

Distance of mass 1 kg from mass M=d3

Distance of mass 1 kg from mass 4M=dx=dd3=2d3

Hence, the correct answers is option (b).

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