Two spheres one of mass `M` has radius `R`. Another sphere has mass `4M` and radius `2R`. The centre to centre distance between them is `12 R`. Find the distance from the centre of smaller sphere where
(a) net gravitational field is zero,
(b) net gravitational potential is half the potential on the surface of larger sphere.

Answer

A, B, D

Explanation

`(GM)/(r^(2)) = (G(4M))/((12 R - r)^(2)`

Solving this equations, we get `r = 4R`
`nu_(P) = (nu_(Q))/(2)`
`:. (-(GM)/(r)) = [(-G(4m))/(12 R - r)]`
`= (-G(4m))/(2R) - (GM)/(10 R)`
solving this equation, we get
`r = 7.65 R` and `1.49 R`