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Question

# Two spherical balls of mass 1 kg and 4 kg are separated by a distance of 12 cm. The distance from 1 kg at which the gravitational force on any mass becomes zero.

A
4cm
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B
12cm
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C
6cm
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D
8cm
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Solution

## The correct option is A 4cmWe know,The gravitational force, F=Gm1m2r2Given,m1=1kgm2=4kgd=12cmLet the distance at which the force due to gravity is 0 is x. This means that force due to both the object at this point are equal and opposite.Distance of this point =xcm from 1kg ball⟹ Distance of this point from 4kg ball =d−x=12−xSo,Gmm1x2=Gmm2(12−x)2⟹1x2=4(12−x)2⟹1x=212−x⟹2x=12−x⟹3x=12⟹x=4cmHence at 4cm from 1kg ball the net force is zero.

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