Discussion Forum



1)

A satellite is revolving in a circular orbit at a height h from the Earth's surface (radius of earth R, h<<R). The minimum I lease in its orbital velocity required so that the satellite could escape from the earth's gravitational field, is close to (neglect the effect of the atmosphere.)


A) $\sqrt{2gR}$

B) $\sqrt{gR}$

C) $\sqrt{gR}/2$

D) $\sqrt{gR}(\sqrt{2}-1)$

Answer:

Option D

Explanation:

$v_{orbital}= \sqrt{\frac{GM}{R}}=\sqrt{gR}$

$v_{escape}= \sqrt{2gR}$

Extra velocity required

           $=v_{escape}-v_{orbital}=\sqrt{gR}(\sqrt{2}-1)$