Question

The radii of circular orbits of two satellites $A$ and $B$ of the earth are $4R$ and $R$ respectively. If the speed of satellite $A$ is $3v$, then the speed of satellite $B$ will be

• A. $3v/4$
• B. $6v$
• C. $12v$
• D. $3v/2$

Answer 1

The correct option is B $6v$


$\frac{m_s{v}^2}{r}=\frac{G{M}_e{m}_s}{r^2}$

$v=\sqrt{\frac{G{M}_e}{r}}=v_0$


$V_{OA}=3v=\sqrt{\frac{G{M}_e}{4R}}$

$V_{OB}=3v^{\prime }=\sqrt{\frac{G{M}_e}{4R}}$

$\frac{3v}{v^{\prime }}=\sqrt{\frac{R_1}{4R_1}}$
$⟹v^{\prime }=6v$