Two stars of masses m1 and m2 are parts of a binary star system. The radii of their orbits are r1 and r2 respectively, measured from the centre of mass of the system. The magnitude of gravitational force m1 exerts on m2 is

Question

Two stars of masses m1 and m2 are parts of a binary star system. The radii of their orbits are r1 and r2 respectively, measured from the centre of mass of the system. The magnitude of gravitational force m1 exerts on m2 is (A) (m1m2G/(r1 + r2)2) (B) (m1G/(r1 + r2)2) (C) (m2G/(r1 + r2)2) (D) (G(m1+m2)/(r1 + r2)2)

Tardigrade Admin · Accepted Answer

The situation is as shown in the figure.

According to Newtons law of gravitation, gravitational force between two bodies of masses

m_{1}

and

m_{2}

is

F = \frac{G m _{1} m _{2}}{r ^{2}}

where

r

is the distance between the two masses.
Here,

r = r_{1} + r_{2}

∴ F = \frac{G m _{1} m _{2}}{( r _{1} + r _{2} ) ^{2}}

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

$\frac{m _{1} m _{2} G}{( r _{1} + r _{2} ) ^{2}}$

$\frac{m _{1} G}{( r _{1} + r _{2} ) ^{2}}$

$\frac{m _{2} G}{( r _{1} + r _{2} ) ^{2}}$

$\frac{G ( m _{1} + m _{2} )}{( r _{1} + r _{2} ) ^{2}}$

Q. Two stars of masses m1​ and m2​ are parts of a binary star system. The radii of their orbits are r1​ and r2​ respectively, measured from the centre of mass of the system. The magnitude of gravitational force m1​ exerts on m2​ is

(r1​+r2​)2m1​m2​G​

(r1​+r2​)2m1​G​

(r1​+r2​)2m2​G​

(r1​+r2​)2G(m1​+m2​)​

The situation is as shown in the figure. According to Newtons law of gravitation, gravitational force between two bodies of masses m1​ and m2​ is F=r2Gm1​m2​​ where r is the distance between the two masses. Here, r=r1​+r2​ ∴F=(r1​+r2​)2Gm1​m2​​

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

$\frac{m _{1} m _{2} G}{( r _{1} + r _{2} ) ^{2}}$

$\frac{m _{1} G}{( r _{1} + r _{2} ) ^{2}}$

$\frac{m _{2} G}{( r _{1} + r _{2} ) ^{2}}$

$\frac{G ( m _{1} + m _{2} )}{( r _{1} + r _{2} ) ^{2}}$