Question

A satellite revolving around in orbit of the Earth at a radius $r$ and a velocity $v$. If the radius of its orbit becomes doubled, Find out its new velocity?

• A. $v/2$
• B. $v/\sqrt{2}$
• C. $v$
• D. $\sqrt{2}v$
• E. $2v$

Answer 1

The correct option is B $v/\sqrt{2}$

Orbital velocity $v$ of a satellite revolving in an orbit of radius $r$ is given by

$v=\sqrt{GM/r}$

now if the radius is doubled , new velocity $v^{\prime }=\sqrt{GM/2r}=\sqrt{GM/r}\times \sqrt{1/2}$

or $v^{\prime }=v/\sqrt{2}$