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 d3,2d3Let 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)(d−x)2=4GM(d−x)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, F−F′=0⇒4GM(d−x)2−GMx2=0⇒4GM(d−x)2=GMx2⇒(d−x)2=4x2⇒d−x=2x⇒x=d3 Distance of mass 1 kg from mass M=d3 Distance of mass 1 kg from mass 4M=d–x=d−d3=2d3 Hence, the correct answers is option (b).

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