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Question

2 bodies having masses 2kg and 4kg respectively are seperated by 2m. Where a body of mass 1kg should be placed so that the gravitational force on this body due to bodies A and B is zero?

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Solution

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=G*2*1/d^2=2G/d^2......1
the gravitational force between B and C is
FBC=GMbMc/d^2=G*4*1/(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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