Two satellites $A$ and $B$ go round a planet $ P$ in circular orbits having radii $4R$ and $R$ respectively. If the speed of the satellite $A$ is $3V$, the speed of the satellite $B$ will be ........ $V$
Two satellites $A$ and $B$ go round a planet $ P$ in circular orbits having radii $4R$ and $R$ respectively. If the speed of the satellite $A$ is $3V$, the speed of the satellite $B$ will be ........ $V$
$12$
$6 $
$\frac{4}{3}$
$\frac{3}{2}$
Two satellites $A$ and $B$ go round a planet $ P$ in circular orbits having radii $4R$ and $R$ respectively. If the speed of the satellite $A$ is $3V$, the speed of the satellite $B$ will be ........ $V$
$v = \sqrt {\frac{{GM}}{R}} $
$\frac{{{v_A}}}{{{v_B}}} = \sqrt {\frac{{{R_B}}}{{{R_A}}}} = \sqrt {\frac{R}{{4R}}} = \frac{1}{2}$
$\frac{{{v_A}}}{{{v_B}}} = \frac{{3V}}{{{v_B}}} = \frac{1}{2}$
$\therefore \,\,{v_B} = 6\,V$
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