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.

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

Answer 1

Answer: (C)

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

Answer 2

The situations is as shown in the figure.

Gravitational force on an object of mass m at point p distance d from centre O lying on the axis of the circular ring of radius R and mass M is given by

When d = r, then

$\mathrm { F } = \frac { \mathrm { GMmR } } { \left( \mathrm { R } ^ { 2 } + \mathrm { R } ^ { 2 } \right) ^ { 3 / 2 } } = \frac { \mathrm { GMmR } } { \left( 2 \mathrm { R } ^ { 2 } \right) ^ { 3 / 2 } } = \frac { \mathrm { GMmR } } { 2 ^ { 3 / 2 } \mathrm { R } ^ { 3 } } = \frac { \mathrm { GMm } } { 2 \sqrt { 2 } \mathrm { R } ^ { 2 } }$