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Two stars of masses m₁ and m₂ are parts of a star system. The radii binary of their orbits are r₁ and r₂ respectively, measured from the centre of mass of the system. The magnitude of gravitational force m₂ exerts on $m_{1}$ , is

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a

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

b

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

c

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

d

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

answer is A.

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Detailed Solution

The situation is as shown in the figure

Question Image

According to Newtons law of gravitation force between two bodies of masses m₁ and m₂ is

$F = \frac{{Gm}_{1} m_{2}}{r^{2}}$

where r is the distance between the two masses.

Here, $r = r_{1} + r_{2} ∴ F = \frac{{Gm}_{1} m_{2}}{{(r_{1} + r_{2})}^{2}}$

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