Question

For the moon to cease to remain the earth's satellite, its orbital velocity has to increase by a factor of

• A. $2$
• B. $\sqrt{2}$
• C. $\frac{1}{\sqrt{2}}$
• D. $-\sqrt{3}$

Answer 1

The correct option is B

$\sqrt{2}$

Orbital velocity and escape velocity:

1. If the moon ceases to be in Earth's orbital, it implies that the orbital velocity is more than the escape velocity.
2. Escape velocity is given by,$v_e=\sqrt{\frac{2Gm}{R}}$
3. Orbital velocity is, $v_0=\sqrt{\frac{Gm}{R}}$
4. Where $G$is the gravitational constant, $m$ is mass of moon and $R$ is the distance from Earth's centre to the Moon
5. So, if orbital velocity increases by factor of $\sqrt{2}$, moon will leave Earth's orbit.

Hence, option B is correct.