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(B) The orbital speed $v$ of a satellite in a circular orbit of radius $r$ is given by the formula $v = \sqrt{\frac{GM}{r}}$,where $G$ is the gravitat

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$6 v$

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(B) The orbital speed $v$ of a satellite in a circular orbit of radius $r$ is given by the formula $v = \sqrt{\frac{GM}{r}}$,where $G$ is the gravitational constant and $M$ is the mass of the planet.This implies that $v \propto \frac{1}{\sqrt{r}}$.Given for satellite $A$: radius $r_A = 4 R$ and speed $v_A = 3 v$.Given for satellite $B$: radius $r_B = R$.Using the proportionality $v_A \sqrt{r_A} = v_B \sqrt{r_B}$,we get:$(3 v) \sqrt{4 R} = v_B \sqrt{R}$.$(3 v) (2 \sqrt{R}) = v_B \sqrt{R}$.$6 v \sqrt{R} = v_B \sqrt{R}$.Therefore,$v_B = 6 v$.

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

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