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Q.
A mass $m$ is placed at point $P$ which 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
Gravitation
Solution:
The situation is as shown in the figure. Gravitational force on an object of mass $m$ at point $P$ at distance d from centre $O$ lying on the axis of the circular ring of radius $R$ and mass $M$ is given by
$F = \frac{GMmd}{\left(R^{2}+d^{2}\right)^{3/2}}$
When $d = R$, then
$F = \frac{GMmR}{\left(R^{2}+R^{2}\right)^{3/2}} = \frac{GMmR}{\left(2R^{2}\right)^{3/2}}$
$= \frac{GMmR}{2^{3*/2}R^{3}} = \frac{GMm}{2\sqrt{2}R^{2}}$
