Question

A planet in a distant solar system is $10$ times more massive than the earth and its radius is $10$ times smaller. Given that the escape velocity from the earth is $11{\text{kms}}^{-1}$, the escape velocity (in ${\text{km s}}^{-1})$ from the surface of the planet would be

• A. 110
• B. 110.0
• C. 110.00

Answer 1

Answer: (A), (B), (C)

Mass of planet, $M_{\text{P}}=10M_{\text{e}}$, where $M_{\text{e}}$ is mass of earth.
Radius of planet, $R_{\text{P}}=\frac{R_{\text{e}}}{10}$, Where $R_{\text{e}}$ is radius of earth.
Escape speed is given by, $v_{\text{P}}=\sqrt{\frac{2GM}{R}}$

For planet, $v_{\text{P}}=\sqrt{\frac{2G\times M_{\text{P}}}{R_{\text{P}}}}$

$v_{\text{P}}=10\times v_{\text{e}}$
$v_{\text{P}}=10\times 11=110{\text{km s}}^{-1}$