Question

Three uniform spheres, each having a mass `M=5kg` and radius `a=2.5m` are kept in such a way that each touches the other two. Find the magnitude of the gravitational force in `GN` on any of the spheres due to the other two.

Answer 1

Correct Answer - 4
The net gravitational force acting due to any two sphere on the third is the vector sum of their individual gravitational force. Therefore,
`F=|vec(F)_(1)+vec(F)_(2)|=sqrt(F_(1)^(2)+F_(2)^(2)+2F_(1)F_(2)cos60^(@))`
Putting `F_(1)=F_(2)rArr F=sqrt(3)F_(1)`
where `F=(G(m)m)/(a^(2))=(Gm^(2))/(a^(2))`
In `G` Newton, `F=(5^(2))/((2.5)^(2))=4`