Two bodies A and B having mass 2 kg and 4 kg respectively, are separated by 2 meters. Where should a body of mass 1 kg be placed so that the gravitational force in this body due to bodies A and B is zero

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Solution

The solution for the query is as follows:
Mass of body a is Ma=2kg

Mass of body b is Mb=4kg

Mass of body cis Mc=1kg

Separation between a and b=2m

Let the body C be placed at a distance d fron the body A,

The gravitational force between A and C,

FAC=GMaMc/d^2=G21/d^2=2G/d^2......1

the gravitational force between B and C is

FBC=GMbMc/d^2=G41/(2-d)^2=4G/(2-d)^2

For body C the gravttatinal force =0

hence Fac=Fbc

2g/d^2=4G/(2-d)^2

(2-d)^2=2d^2

2-d=√2d

(√2+1)d=2

d=0.83m

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