Two rings having masses `M` and `2M` respectively, having the same radius are placed coaxially as shown in the figure.
If the mass distribution on both the rings is non-uniform, then the gravitational potential at point `P` is

Options

A. `-(GM)/R[1/(sqrt(2))+2/(sqrt(5))]`
B. `-(GM)/R[1+2/2]`
C. zero
D. cannot be determined from given information

Answer

A

Explanation

As all the point on the periphery of either ring are at same distance from point `P`, the potential at point `P` due to whole ring can be calculate as `V=-(GM)//(sqrt(R^(2)+x^(2)))` where `x` is axial distance from the centre of the ring. This expression is independent of the fact whether the distribution of mass is uniform or non-uniform.
So, `V` at `P` is `V=-(GM)/(sqrt(2)R)-(Gxx2M)/(sqrt(5)R)`
`=-(GM)/R[1/(sqrt(2))+2/(sqrt(5))]`.