Question

Two rings having masses M and $2$M, 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?

• A. $-\frac{GM}{R}[\frac{1}{\sqrt{2}}+\frac{2}{\sqrt{5}}]$
• B. $-\frac{GM}{R}[1+\frac{2}{2}]$
• C. Zero
• D. Cannot be determined from the given information

Answer 1

The correct option is A $-\frac{GM}{R}[\frac{1}{\sqrt{2}}+\frac{2}{\sqrt{5}}]$

Gravitational potential due to a ring of mass $M$ at distance $x$ on axis of radius $R$ is

$V=-\frac{GM}{\sqrt{R^2+x^2}}\therefore V_p=-\frac{GM}{\sqrt{R^2+R^2}}-\frac{2GM}{\sqrt{R62+4R^2}}{V}_p=-\frac{GM}{R}[\frac{1}{\sqrt{2}}+\frac{2}{\sqrt{5}}]$