Question

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

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

Answer 1

Answer: (C)

$6v$

Answer 2

The orbital speed of a satellite is given by:
$v = \sqrt{\frac{GM}{R}}.$
For satellites $A$ and $B$:
$\frac{v_A}{v_B} = \sqrt{\frac{R_B}{R_A}} = \sqrt{\frac{R}{4R}} = \frac{1}{2}.$
Thus:
$v_B = 2v_A.$
Given $v_A = 3v$, the speed of $B$ is:
$v_B = 2 \cdot 3v = 6v.$