Question 90: Gravitation

Question

The mass of the moon is $$\frac{1}{144}$$ times the mass of a planet and its diameter is $$\frac{1}{16}$$ times the diameter of a planet. If the escape velocity on the planet is $$v$$, the escape velocity on the moon will be :

Accepted Answer

$$\begin{aligned}
& \mathrm{V}_{	ext {escape }}=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}} \
& \mathrm{V}_{	ext {planet }}=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}}=\mathrm{V} \
& \mathrm{V}_{	ext {Moon }}=\sqrt{\frac{2 \mathrm{GM} 	imes 16}{144 \mathrm{R}}}=\frac{1}{3} \sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}} \
& \mathrm{V}_{	ext {Moon }}=\frac{\mathrm{V}_{	ext {Planet }}}{3}=\frac{\mathrm{V}}{3}
\end{aligned}$$

Answer

$$\frac{\mathrm{v}}{4}$$

Answer

$$\frac{\mathrm{v}}{6}$$

Answer

$$\frac{\mathrm{V}}{12}$$

Answer

$$\frac{\mathrm{v}}{3}$$

Gravitation

The mass of the moon is $\frac{1}{144} times the mass of a planet and its diameter is \frac{1}{16} times the diameter of a planet. If the escape velocity on the planet is v$, the escape velocity on the moon will be :

Choose the correct answer: