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

The Correct Option is C

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:
\[v_B = 2 \cdot 3v = 6v.\]