Gravitation Question 8
Question 8 - 2024 (30 Jan Shift 2)
Escape velocity of a body from earth is $11.2 \mathrm{~km} / \mathrm{s}$. If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the plate is:
(1) $11.2 \mathrm{~km} / \mathrm{s}$
(2) $8.4 \mathrm{~km} / \mathrm{s}$
(3) $4.2 \mathrm{~km} / \mathrm{s}$
(4) $7.9 \mathrm{~km} / \mathrm{s}$
Show Answer
Answer: (4)
Solution:
$R_{P}=\frac{R_{E}}{3}, M_{P}=\frac{M_{E}}{6}$
$\mathrm{V}{\mathrm{e}}=\sqrt{\frac{2 \mathrm{GM}{\mathrm{e}}}{\mathrm{R}_{\mathrm{e}}}}$
$\mathrm{V}{\mathrm{P}}=\sqrt{\frac{2 \mathrm{GM}{\mathrm{P}}}{\mathrm{R}_{\mathrm{P}}}}$
$\frac{\mathrm{V}{\mathrm{e}}}{\mathrm{V}{\mathrm{p}}}=\sqrt{2}$
$\mathrm{V}{\mathrm{P}}=\frac{\mathrm{V}{\mathrm{e}}}{\sqrt{2}}=\frac{11.2}{\sqrt{2}}=7.9 \mathrm{~km} / \mathrm{sec}$
