Question

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

• A. $12v$
• B. $6v$
• C. $\frac{4}{3}v$
• D. $\frac{3}{2}v$

Answer 1

The correct option is B $6v$

The orbital velocity of a satellite in circular orbit of radius $R$ around a planet of mass $M$ is given by $$v=\sqrt{\frac{GM}{R}}$$ $\Rightarrow \frac{v_A}{v_B}=\sqrt{\frac{R_B}{R_A}}$

Substituting $R_A=4R$ and $R_B=R$

$\Rightarrow \frac{v_A}{v_B}=\sqrt{\frac{R}{4R}}$

$\Rightarrow v_B=2v_A$

Given, $v_A=3v$

$\Rightarrow v_b=2\times 3v$

$\therefore v_B=6v$

Hence, option (b) is the correct answer.

Key Concept: The orbital velocity of a satellite is given by $$v=\sqrt{\frac{GM}{r}}$$