Question

The escape velocity for the earth is $11.2 \,km / sec$. The mass of another planet $100$ times mass of earth and its radius is $4$ times radius of the earth. The escape velocity for the planet is:

• A. 56.0 km/sec
• B. 280 km/sec
• C. 112 km/sec
• D. 56 km/sec

Answer 1

Answer: (A)

56.0 km/sec

Answer 2

$v_{\text {escape }}=\sqrt{\frac{2 G M}{R}} \propto \sqrt{\frac{M}{R}}$, Hence, $\frac{v_{p}}{v_{e}}=\sqrt{\frac{M_{p}}{R_{p}} \times \frac{R_{e}}{M_{e}}}$ or $\frac{v_{p}}{v_{e}}=\sqrt{100 \times \frac{1}{4}}=5$ $v_{p}=5 \times 11.2=56 \,km / sec$