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

Question

Two satellites A and B go round a planet P in circular orbits having radii 4R and R respectively. If the speed of satellite A is 3V , the speed of the satellite B will be. (A) 12V (B) 6V (C) (4/3) V (D) (3/2) V

Tardigrade Admin · Accepted Answer

v = √(G M/R) ⇒ (vA/vB) = √(RB/RA) = √(R/4 R) = (1/2) ∴ (vA/vB) = (3 V/vB) = (1/2) ∴ vB = 6 V

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

$12 V$

$6 V$

$\frac{4}{3} V$

$\frac{3}{2} V$

$v = \frac{GM}{R}$ $\Rightarrow$ $\frac{v _{A}}{v _{B}} = \frac{R _{B}}{R _{A}} = \frac{R}{4 R}$ $= \frac{1}{2}$
$∴ \frac{v _{A}}{v _{B}} = \frac{3 V}{v _{B}} = \frac{1}{2}$
$∴ v_{B} = 6 V$

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

12V

6V

34​V

23​V