Gravitation Question 10
Question 10 - 2024 (31 Jan Shift 2)
The mass of the moon is $1 / 144$ times the mass of a planet and its diameter $1 / 16$ times the diameter of a planet. If the escape velocity on the planet is $v$, the escape velocity on the moon will be:
(1) $\frac{v}{3}$
(2) $\frac{v}{4}$
(3) $\frac{v}{12}$
(4) $\frac{v}{6}$
Show Answer
Answer: (1)
Solution:
$\mathrm{V}_{\text {escape }}=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}}$
$\mathrm{V}_{\text {planet }}=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}}=\mathrm{V}$
$\mathrm{V}_{\text {Moon }}=\sqrt{\frac{2 \mathrm{GM} \times 16}{144 \mathrm{R}}}=\frac{1}{3} \sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}}$
$\mathrm{V}{\text {Moon }}=\frac{\mathrm{V}{\text {Planet }}}{3}=\frac{\mathrm{V}}{3}$
