Question

The mass of a planet is half that of the earth and the radius of the planet is one-fourth that of earth. If we plan to send an artificial satellite from the planet, the escape velocity will be, (escape velocity on earth $v_e=11km-s^{-1}$ )

• A. $11km-s^{-1}$
• B. $5.5km-s^{-1}$
• C. $15.55km-s^{-1}$
• D. $7.78km-s^{-1}$

Answer 1

Answer: (C)

Escape velocity
$v_{es}=\sqrt{\frac{2GM}{R}}$
$\Rightarrow \frac{v_1}{v_2}=\sqrt{\frac{M_1}{M_2}\times \frac{R_2}{R_1}}$
$\Rightarrow \frac{v_1}{v_2}=\sqrt{\frac{M_1}{\frac{M_1}{2}}\times \frac{\frac{R_1}{4}}{R_1}}=\frac{1}{\sqrt{2}}$
$\Rightarrow v_2=\sqrt{2}\times 11=15.55km{s}^{-1}$