Question

A uniform ring of mass $m$ is lying at a distance $a$ from the centre of a sphere of mass $M$ just over the sphere (where $a$ is the radius of the ring as well as that of the sphere). Then magnitude of gravitational force between them is
6

• A. $\frac{GMm}{2\sqrt{2}{a}^2}$
• B. $\sqrt{3}\frac{GMm}{8a^2}$
• C. $\frac{GMm}{8a^2}$
• D. $\sqrt{2}\frac{GMm}{a^2}$

Answer 1

The correct option is A $\frac{GMm}{2\sqrt{2}{a}^2}$

Electric field due to the ring at centre of the sphere
$E=\frac{Gmx}{(x^2+r^2{)}^{\frac{3}{2}}}$
($r$ - radius of the ring)
($x$ - distance from the centre of the ring)
$E=\frac{Gma}{(a^2+a^2{)}^{\frac{3}{2}}}$
$E=\frac{Gma}{2\sqrt{2}{a}^3}$
$E=\frac{Gm}{2\sqrt{2}{a}^2}$
Assuming sphere to be a point mass$F=\frac{GMm}{2\sqrt{2}{a}^2}$