Question

Two stars of masses are parts of a binary star system. The radii of their orbits are $\mathrm { r } _ { 1 }$ and $\mathrm { r } _ { 2 }$ respectively, measured from the centre of mass of the system. The magnitude of gravitational force exerts on is

• A. $\frac { \mathrm { m } _ { 1 } \mathrm {~m} _ { 2 } \mathrm { G } } { \left( \mathrm { r } _ { 1 } + \mathrm { r } _ { 2 } \right) }$
• B.
• C.
• D.

Answer 1

Answer: (A)

$\frac { \mathrm { m } _ { 1 } \mathrm {~m} _ { 2 } \mathrm { G } } { \left( \mathrm { r } _ { 1 } + \mathrm { r } _ { 2 } \right) }$

Answer 2

The situation is as shown in the figure.

According to Newton’s law of gravitations, gravitational force between two bodies of masses

and $\mathrm { m } _ { 2 }$ is

Where r is the distance between the two masses.

Hence, $\therefore \mathrm { F } = \frac { \mathrm { Gm } _ { 1 } \mathrm {~m} _ { 2 } } { \left( \mathrm { r } _ { 1 } + \mathrm { r } _ { 2 } \right) ^ { 2 } }$