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

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

Answer 1

The correct option is A $110km{s}^{-1}$

$Escapevelocity=\sqrt{\frac{2Gm}{r}}\frac{v_{new}}{v_{earth}}=\sqrt{\frac{m_{new}{r}_{earth}}{m_{earth}{r}_{new}}}=\sqrt{\frac{10}{\frac{1}{10}}}=10v_{new}=110km{s}^{-1}$