Two satellite (I) and (II) are moving round a planet in circular orbit having radii R and 3R respectively, if the speed of satellite (I) is v the speed of satellite B will be
Answer & explanation
Correct answer: option 3
$T=2 \pi r / v$
$T=2 \pi R / v_1 $ and $T_2=2 \pi 3 R / v_2 $
$\frac{T_1}{T_2}=\frac{1}{3}\left(\frac{v_2}{v_1}\right)$
$\left(\frac{T_1}{T_2}\right)^2=\frac{1}{9}\left(\frac{v_2}{v_1}\right)^2$
But by Kepler's third law $\frac{T_1^2}{T_2^2}=\left(\frac{R_1}{R_2}\right)^3=\left(\frac{1}{3}\right)^3$
$\left(\frac{1}{3}\right)^3=\frac{1}{9}\left(\frac{v_2}{v_1}\right)^2 \Rightarrow v_2=\frac{v_1}{\sqrt{3}}$