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)/(sqrt(2)) ] `
C. zero
D. connot be determined from the given information

Answer

A

Explanation

As all the points on the periphery of either ring are at 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 axial distance from the centre of the ring. This expression is independent of the fact whether the distribution of mass of uniform or non-uniform.
So, at P, V = - `(GM)/(sqrt(2) R) - (G xx 2M)/(sqrt(5) R) = - (GM)/(R) [ (1)/(sqrt(2)) + (2)/(sqrt(5)) ] `