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/sqrt2+2/sqrt(5)]`
B. `-(GM)/R[1+2/2]`
C. zero
D. cannot be determined from the given information

Answer

A

Explanation

As all the points on the periphery of eigher ring are the same distance from point `P`, the potential at point `P` due to the whole ring can be calculated as `V=-(GM)//(sqrt(R^(2)+x^(2)))` where `x` is the axis 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 at `P,V=-(GM)/(sqrt(2)R)-(Gxx2M)/(sqrt(5)R)=-(GM)/R[1/(sqrt(2))+2/(sqrt(5))]`