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

The Correct Option is B

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: 
v_A = \(\sqrt{\frac {GM}{4R}}\)
For satellite B: 
v_B = \(\sqrt{\frac {GM}{R}}\)
v_A = \(\sqrt{\frac {GM}{4R}}\) 
v_A  = \(\sqrt{\frac {1}{4}}\) \(\sqrt{\frac {GM}{R}}\) 
v_A   = \(\frac {1}{2}\)v_B 
Therefore, the speed of satellite B is twice the speed of satellite A, which means:
v_B = 2 v_A 
v_B = 2 x 3V 
v_B = 6V 
So, the correct option is (B) 6V.