Q: A body is moving in a low circular orbit bout a planet of mass M and radius R . The radius of the orbit can be taken to be R itself . Then ratio of the speed of this body in the orbit to the escape velocity from the planet is

(a) $\sqrt{2}$

(b) 2

(c) $\frac{1}{\sqrt{2}}$

(d) 1

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Ans: (c)

Sol: Orbital velocity $\large v_o = \sqrt{\frac{G M}{R}}$ …(i)

Escape velocity $\large v_e = \sqrt{\frac{2 G M}{R}}$ …(ii)

On dividing ,

$\large \frac{v_o}{v_e} = \sqrt{\frac{1}{\sqrt{2}}}$