Question 29: Gravitation

Question

If escape velocity on earth surface is $$11.1 \mathrm{~kmh}^{-1}$$, then find the escape velocity on moon surface. If mass of moon is $$\frac{1}{81}$$ times of mass of earth and radius of moon is $$\frac{1}{4}$$ times radius of earth.

Accepted Answer

Given, Escape velocity on the surface of the earth is given by
i.e:
$$\begin{aligned}
& v_e=\sqrt{2 g R_e} \
& v_e=\sqrt{\frac{2 G M_e}{R_e}} \quad 	ext{.... (i)}
\end{aligned}$$
Mass of the moon, $$M_m=\frac{M_e}{81}$$
Radius of the moon, $$R_m=\frac{R_e}{4}$$
$$	herefore$$ Escape velocity on the surface of the moon
$$v_m=\sqrt{\frac{2 G M_m}{R_m}}=\sqrt{\frac{2 G\left(\frac{M e}{81}ight)}{\frac{R_e}{4}}}=\frac{2 \sqrt{2}}{9} \sqrt{\frac{G M_e}{R_e}}$$
From Eq. (i),
$$=\frac{2}{9} \sqrt{\frac{2 G M_e}{R_e}}=\frac{2}{9} v_e$$
Escape velocity $$v_e=11.1 \mathrm{~km} / \mathrm{h}$$
$$=\frac{2}{9} 	imes 11.1=2.46 \mathrm{~km} \mathrm{~h}^{-1}$$

Answer

$$2.46 \mathrm{~kmh}^{-1}$$

Answer

$$3.46 \mathrm{~kmh}^{-1}$$

Answer

$$4.4 \mathrm{~kmh}^{-1}$$

Answer

None of these

Gravitation

If escape velocity on earth surface is $11.1 \mathrm{~kmh}^{-1}, then find the escape velocity on moon surface. If mass of moon is \frac{1}{81} times of mass of earth and radius of moon is \frac{1}{4}$ times radius of earth.

Choose the correct answer: