Question

Two satellites A and B rotate round a planet’s orbit having radius 4R and R respectively. If the speed of satellite A is 3 V then speed of satellite B is

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

Answer 1

Answer: (B)

6V

Answer 2

The speed of an object in a circular orbit is given by the formula:
v = $\sqrt{\frac {GM}{R}}$
Let's compare the speeds of satellites A and B: For satellite A:
vA = $\sqrt{\frac {GM}{4R}}$
For satellite B:
vB = $\sqrt{\frac {GM}{R}}$
vA = $\sqrt{\frac {GM}{4R}}$
vA = $\sqrt{\frac {1}{4}}$ $\sqrt{\frac {GM}{R}}$
vA = $\frac {1}{2}$vB
Therefore, the speed of satellite B is twice the speed of satellite A, which means:
vB = 2 vA
vB = 2 x 3V
vB = 6V
So, the correct option is (B) 6V.