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 $11 \, km \, s^{- 1}$ , the escape velocity from the surface of the planet would be

• A. $0.11kms^{- 1}$
• B. $1.1 \, km \, s^{- 1}$
• C. $11 \, km \, s^{- 1}$
• D. $110 \, km \, s^{- 1}$

Answer 1

Answer: (D)

$v_{\text{escape}}=\sqrt{\frac{2 \textit{GM}}{\textit{R}}}$ for the earth
$v_{e}=11kms^{- 1}$
Mass of the planet = $10M_{e}$ .
Radius of the planet = $\frac{R}{10}$ .
$\therefore $ $v_{e}=\sqrt{\frac{2 \textit{GM} \times 1 0}{\textit{R} / \text{10}}}=\text{10}\times \text{11}=110\text{ km}\text{ s}^{- 1}$