Question

Two satellites \(A\) and \(B\) of same mass are revolving round the earth at height \(2R\) and \(3R\) respectively above the surface of the earth. The ratio of kinetic energies of \(A\) to \(B\) will be

• A. \(3:2\)
• B. \(3:4\)
• C. \(2:3\)
• D. \(4:3\)

Hint:

Kinetic energy of a satellite in circular orbit is inversely proportional to orbital radius.

Answer 1

The Correct Option is D

Step 1: Expression for kinetic energy of satellite.
For a satellite in circular orbit, \[ K = \frac{GMm}{2r}. \]
Step 2: Orbital radii.
\[ r_A = R + 2R = 3R, \quad r_B = R + 3R = 4R. \]
Step 3: Ratio of kinetic energies.
\[ \frac{K_A}{K_B} = \frac{r_B}{r_A} = \frac{4R}{3R} = \frac{4}{3}. \]
Step 4: Conclusion.
The ratio of kinetic energies is \(4:3\).