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 from the surface of the planet would be

• A. $1.1{\text{kms}}^{–1}$
• B. $11{\text{kms}}^{–1}$
• C. $110{\text{kms}}^{–1}$
• D. $0.11{\text{kms}}^{–1}$

Answer 1

The correct option is C $110{\text{kms}}^{–1}$

Mass of planet, $M_p=10M_e$, where $M_e$ is mass of earth.
Radius of planet, $R_p=\frac{R_e}{10}$, where $R_e$ is radius of earth.
Escape speed is given by, $v_P=\sqrt{\frac{2GM}{R}}$
For planet, $v_P=\sqrt{\frac{2G\times M_P}{R_P}}=\sqrt{\frac{100\times 2G{M}_e}{R_e}}$
$=10\times v_e$
$=10\times 11=110{\text{Kms}}^{-1}$