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

Question

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 (A) (GMm/√2R2) (B) (GMm/2R2) (C) (GMm/2√2R2) (D) (GMm/4R2)

Tardigrade Admin · Accepted Answer

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{GM m d}{( R ^{2} + d ^{2} ) ^{3/2}}

When

d = R

, then

F = \frac{GM m R}{( R ^{2} + R ^{2} ) ^{3/2}} = \frac{GM m R}{( 2 R ^{2} ) ^{3/2}}

= \frac{GM m R}{2 ^{3 * /2} R ^{3}} = \frac{GM m}{2 2 R ^{2}}

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

$\frac{GM m}{2 R ^{2}}$

$\frac{GM m}{2 R ^{2}}$

$\frac{GM m}{2 2 R ^{2}}$

$\frac{GM m}{4 R ^{2}}$

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

2​R2GMm​

2R2GMm​

22​R2GMm​

4R2GMm​

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=(R2+d2)3/2GMmd​ When d=R, then F=(R2+R2)3/2GMmR​=(2R2)3/2GMmR​ =23∗/2R3GMmR​=22​R2GMm​

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

$\frac{GM m}{2 R ^{2}}$

$\frac{GM m}{2 R ^{2}}$

$\frac{GM m}{2 2 R ^{2}}$

$\frac{GM m}{4 R ^{2}}$