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

Answer 1

Answer: (D)

${110 \, km \, s^{-1}}$

Answer 2

Escape velocity from the surface of the earth is
$\upsilon_e = \sqrt{\frac{2GM}{R}}$
$\upsilon_e = 11 \, km \, s^{-1}$
Mass of the planet = $10M$.
Radius of the planet = $R/10$.
$\therefore \, \upsilon_p = \sqrt{\frac{2GM \times 10}{R/10}} = 10 \upsilon_e = 10 \times 11$
$= { 110 \, km \, s^{-1}}$