Question

The ratio of the radius of the Earth to that of the moon is $10:1$. The ratio of g on earth to the moon is 6. The ratio of the escape velocity from the earth’s surface to that from the moon is approximately

• A. 8
• B. 2
• C. 4
• D. 10

Answer 1

The correct option is A 8

Given,
$\frac{r_e}{r_m}=10$ and $\frac{g_e}{g_m}=6$
Escape velocity is given as,
$V_e=\sqrt{2gr}$
$\frac{V_e}{V_m}=\frac{\sqrt{2g_e{r}_e}}{\sqrt{2g_m{r}_m}}$
$\frac{V_e}{V_m}=\sqrt{\frac{g_e}{g_m}\times \frac{r_e}{r_m}}$
$\frac{V_e}{V_m}=\sqrt{6\times 10}$
$\frac{V_e}{V_m}\approx 8$