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
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
\(\frac {3V}{2}\)
6V
\(\frac {4V}{2}\)
12 V
The Correct Option is B
Solution and Explanation
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.
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