Question

If $r$ represents the radius of the orbit of the satellite of mass $m$ moving around planet of mass $M$, then the velocity of satellite $v$ is obtained from the relation:

• A. $v=\frac{G Mm}{r}$
• B. $ v =\frac{Gm}{r} $
• C. $v^{2}=\frac{Gm}{r} $
• D. $v =\frac{GM}{r} $

Answer 1

Answer: (C)

Here : Radius of orbit $=r$
Mass of the satellite $=m$
Mass of the planet $=M$
Velocity of satellite $=v$
when a satellite moves in an orbit.
Its gravitational force is balanced by the centripetal force, thus,
$\frac{G M m}{r^{2}}=\frac{m v^{2}}{r}$
(where $G$ is universal constant)
or $v^{2}=\frac{G M}{r}$