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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
$\frac{3V}{2}$
B
$\frac{3V}{4}$
C
6V
D
12V
Detailed Solution
Orbital speed of a satellite in a circular orbit of radius r: $v = \sqrt{\frac{GM}{r}}$, so $v \propto \frac{1}{\sqrt{r}}$
$\frac{v_B}{v_A} = \sqrt{\frac{r_A}{r_B}} = \sqrt{\frac{4R}{R}} = 2$
$v_B = 2v_A = 2\times3V$
$v_B = 6V$
$\frac{v_B}{v_A} = \sqrt{\frac{r_A}{r_B}} = \sqrt{\frac{4R}{R}} = 2$
$v_B = 2v_A = 2\times3V$
$v_B = 6V$