Question

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

• A. $\sqrt{\frac{Gm}{d}}$
• B. $\sqrt{\frac{2Gm}{d}}$
• C. $\sqrt{\frac{Gm}{2d}}$
• D. $\sqrt{\frac{Gm}{4d}}$

Answer 1

The correct option is C $\sqrt{\frac{Gm}{2d}}$

Here centripital force is provided by gravitational force of attraction. So,
ceptripetal force $=$ Gravitational force

$\frac{m{v}^2}{\left(\frac{d}{2}\right)}=\frac{Gmm}{d^2}$
$⟹v=\sqrt{\frac{Gm}{2d}}$