Two stars both of mass are orbiting their common $C O M$ . If the distance between them is d , tangential velocity of both the stars are

\sqrt{\frac{G m}{d}}

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\sqrt{\frac{2 G m}{d}}

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\sqrt{\frac{G m}{2 d}}

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\sqrt{\frac{G m}{4 d}}

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Solution

The correct option is C $\sqrt{\frac{G m}{2 d}}$
Here centripital force is provided by gravitational force of attraction. So,
ceptripetal force $=$ Gravitational force

$\frac{m v^{2}}{(\frac{d}{2})} = \frac{G m m}{d^{2}}$
$⟹ v = \sqrt{\frac{G m}{2 d}}$

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Two stars both of mass are orbiting their common COM. If the distance between them is d , tangential velocity of both the stars are

The correct option is C √Gm2dHere centripital force is provided by gravitational force of attraction. So, ceptripetal force = Gravitational force mv2(d2)=Gmmd2 ⟹v=√Gm2d

Two stars both of mass are orbiting their common $C O M$ . If the distance between them is d , tangential velocity of both the stars are

The correct option is C $\sqrt{\frac{G m}{2 d}}$
Here centripital force is provided by gravitational force of attraction. So,
ceptripetal force $=$ Gravitational force

$\frac{m v^{2}}{(\frac{d}{2})} = \frac{G m m}{d^{2}}$
$⟹ v = \sqrt{\frac{G m}{2 d}}$