Question

Two satellites $A$ and $B$ go round the planet $P$ in circular orbits having radii $4R$ and $R$ respectively. If the speed of the satellite $A$ is $3v$, then the speed of satellite $B$ will be

• A. $6v$
• B. $12v$
• C. $\frac{3v}{2}$
• D. $\frac{4v}{3}$

Answer 1

The correct option is A $6v$

Velocity $v$ of a satellite varies inversely as the square root of the orbit of radius $r$
$v\propto \frac{1}{\sqrt{r}}$
$\therefore \frac{V_A}{V_B}=\sqrt{\frac{r_B}{r_A}}=\sqrt{\frac{R}{4R}}$
$\Rightarrow \frac{3v}{V_B}=\frac{1}{2}\Rightarrow V_B=6v$