JEE MAIN - Physics (2024 - 31st January Evening Shift - No. 19)
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 :
$$\frac{\mathrm{v}}{4}$$
$$\frac{\mathrm{v}}{6}$$
$$\frac{\mathrm{V}}{12}$$
$$\frac{\mathrm{v}}{3}$$
Explanation
$$\begin{aligned}
& \mathrm{V}_{\text {escape }}=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}} \\
& \mathrm{V}_{\text {planet }}=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}}=\mathrm{V} \\
& \mathrm{V}_{\text {Moon }}=\sqrt{\frac{2 \mathrm{GM} \times 16}{144 \mathrm{R}}}=\frac{1}{3} \sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}} \\
& \mathrm{V}_{\text {Moon }}=\frac{\mathrm{V}_{\text {Planet }}}{3}=\frac{\mathrm{V}}{3}
\end{aligned}$$
Comments (0)
