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 $11\text{km/s}$, the escape velocity from the surface of the planet would be

• A. $1.1\text{km/s}$
• B. $11\text{km/s}$
• C. $110\text{km/s}$
• D. $0.11\text{km/s}$

Answer 1

The correct option is C $110\text{km/s}$

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, $V_e=\sqrt{\frac{2G{M}_e}{R_e}}=11\text{km/s}$
For planet, $V_P=\sqrt{\frac{2G\times M_P}{R_P}}=\sqrt{\frac{100\times 2G{M}_e}{R_e}}$
$=10\times V_e$
$=10\times 11=110\text{Km/s}$