Two satellites A and B go round a planet in c | vedclass

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Question

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

Vedclass · Accepted Answer

$6v$

Vedclass · Answer

(C) The orbital speed of a satellite in a circular orbit is given by the formula $v = \sqrt{\frac{GM}{r}}$,where $G$ is the gravitational constant,$M$ is the mass of the planet,and $r$ is the radius of the orbit.From this relation,we see that $v \propto \frac{1}{\sqrt{r}}$.Therefore,the ratio of the speeds of satellites $A$ and $B$ is $\frac{v_B}{v_A} = \sqrt{\frac{r_A}{r_B}}$.Given $r_A = 4R$ and $r_B = R$,we have $\frac{v_B}{v_A} = \sqrt{\frac{4R}{R}} = \sqrt{4} = 2$.Given the speed of satellite $A$ is $v_A = 3v$,the speed of satellite $B$ is $v_B = 2 	imes v_A = 2 	imes 3v = 6v$.

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

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