Question 300: Gravitation

Question

The radius and mean density of the planet are four times as that of the earth. The ratio of escape velocity at the earth to the escape velocity at a planet is

Accepted Answer

$$\begin{aligned}
& v_c=\sqrt{\frac{2 G M}{R}} \
& v_c=R \sqrt{\frac{8}{3} \pi G ho} \ldots .\left(\because M=\frac{4}{3} \pi R^3 hoight) \
& 	ext { Also, } ho_p=4 ho_E 	ext { and } R_p=4 R_E \
& \frac{v_c}{v_p}=\frac{R_E \sqrt{ho_E}}{4 R_E \sqrt{4 ho_E}}=\frac{1}{8}=1: 8
\end{aligned}$$

Answer

$1: \sqrt{8}$

Answer

$1: 8$

Answer

$1: \sqrt{3}$

Answer

$1: 3$

Gravitation

The radius and mean density of the planet are four times as that of the earth. The ratio of escape velocity at the earth to the escape velocity at a planet is

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