Question 76: Gravitation

Question

Escape velocity of a body from earth is $$11.2 \mathrm{~km} / \mathrm{s}$$. If the radius of a planet be onethird the radius of earth and mass be one-sixth that of earth, the escape velocity from the planet is :

Accepted Answer

$$\begin{aligned}
& \mathrm{R}_{\mathrm{P}}=\frac{\mathrm{R}_{\mathrm{E}}}{3}, \mathrm{M}_{\mathrm{P}}=\frac{\mathrm{M}_{\mathrm{E}}}{6} \
& \mathrm{~V}_{\mathrm{c}}=\sqrt{\frac{2 \mathrm{GM}_{\mathrm{e}}}{\mathrm{R}_{\mathrm{e}}}} \quad 	ext{.... (i)}\
& \mathrm{V}_{\mathrm{P}}=\sqrt{\frac{2 \mathrm{GM}_{\mathrm{P}}}{\mathrm{R}_{\mathrm{P}}}} \quad 	ext{.... (ii)}\
& \frac{\mathrm{V}_{\mathrm{e}}}{\mathrm{V}_{\mathrm{p}}}=\sqrt{2} \
& \mathrm{~V}_{\mathrm{P}}=\frac{\mathrm{V}_{\mathrm{e}}}{\sqrt{2}}=\frac{11.2}{\sqrt{2}}=7.9 \mathrm{~km} / \mathrm{sec}
\end{aligned}$$

Answer

7.9 km/s

Answer

8.4 km/s

Answer

4.2 km/s

Answer

11.2 km/s

Gravitation

Escape velocity of a body from earth is $11.2 \mathrm{~km} / \mathrm{s}$. If the radius of a planet be onethird the radius of earth and mass be one-sixth that of earth, the escape velocity from the planet is :

Choose the correct answer: