Question

A mass m is placed at point P lies on the axis of a ring of mass M and radius R at a distance R from its centre. The gravitational force on mass m is then

• A. $\frac{GMm}{\sqrt{2}{R}^2}$
• B. $\frac{GMm}{2R^2}$
• C. $\frac{GMm}{2\sqrt{2}{R}^2}$
• D. $\frac{GMm}{4R^2}$

Answer 1

The correct option is C $\frac{GMm}{2\sqrt{2}{R}^2}$

The situation is as shown in the figure.

The gravitational force on an an object of mass m at point p distanced from center O lying on the axis of the circular ring of radius R and mass M is given by
$F={\frac{GMmd}{(R^2+d^2)}}^{3/2}$

When d=R, then
$F=\frac{GMmR}{{(R^2+R^2)}^{3/2}}$

$=\frac{GMmR}{{\left({2R}^2\right)}^{3/2}}$

$=\frac{GMmR}{2^{3/2}{R}^3}$

$=\frac{GMm}{2\sqrt{2}{R}^2}$