Question

A body of mass 1 kg is placed at a distance of 2m from another body of mass 10kg. At what distance from the body of 1kg, another body of mass 5kg be placed so that the net force of gravitation acting on the body of mass 1kg is zero?

Answer 1

Here mass of body`A,m_(1)=1kg`, mass of body B,`m_(2)=10kg`
Distance between bodies A and B, `r_(1)=2m`, mass of another body `C,m=5kg`
Let distance of body C from body A be
`AC=r_(2)=x`,

As net force of gravitation acting on the body A of mass 1kg is zero, therefore,
force of attraction of B on A = force of attraction of C on A, i.e., `F_(1)=F_(2)`
or `(Gm_(1) m_(2))/(r_(1)^(2)) = (Gm_(1)m)/(r_(2)^(2))` or `(m_(2))/(r_(1)^(2))=m/(r_(2)^(2))`
or `(10)/((2)^(2))=(5)/(x^(2))` or `x^(2) = (5xx2^(2))/(10)=2` or `x=sqrt2m`