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Newton's Law of Gravitation

Two stars of ...

Question

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 then

\frac{m_{1} m_{2} G}{{(r_{1} + r_{2})}_{1}^{2}}

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\frac{m_{1} G}{{(r_{1} + r_{2})}_{1}^{2}}

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\frac{m_{2} G}{{(r_{1} + r_{2})}_{1}^{2}}

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\frac{G (m_{1} + m_{2})}{{(r_{1} + r_{2})}_{1}^{2}}

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Solution

The correct option is B $\frac{m_{1} m_{2} G}{{(r_{1} + r_{2})}_{1}^{2}}$
The situation is as shown in the figure. According to Newton's 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, $r = r_{1} + r_{2} ∴ F = \frac{G m_{1} m_{2}}{{(r_{1} + r_{2})}_{1}^{2}}$

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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 then

The correct option is B m1m2G(r1+r2)2The situation is as shown in the figure. According to Newton's law of gravitation, gravitational force between two bodies of masses m1 and m2 is F=Gm1m2r2Where r is the distance between the two masses.Here, r=r1+r2∴F=Gm1m2(r1+r2)2

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 then