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 $v_{e}=11\, km - s ^{-1}$ )

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

Answer 1

Answer: (C)

Escape velocity
$v_{ es }=\sqrt{\frac{2 G M}{R}}$
$\Rightarrow \frac{v_{1}}{v_{2}}=\sqrt{\frac{M_{1}}{M_{2}} \times \frac{R_{2}}{R_{1}}}$
$\Rightarrow \frac{v_{1}}{v_{2}}=\sqrt{\frac{M_{1}}{\frac{M_{1}}{2}} \times \frac{\frac{R_{1}}{4}}{R_{1}}}=\frac{1}{\sqrt{2}}$
$\Rightarrow v_{2}=\sqrt{2} \times 11=15.55\, kms ^{-1}$