Question

Ratio of the radius of the earth to that of the moon is $10$. Ratio of $g$ on the earth to the moon is $6$. Then ratio of the escape velocity from the earth's surface to that from the moon is approximately

• A. $2$
• B. $4$
• C. $8$
• D. $10$

Answer 1

The correct option is C $8$

Escape velocity, $v_e=\sqrt{2gR}$
For moon, $v_{e,moon}=\sqrt{2gR}$
For earth, $v_{e,moon}=\sqrt{2\times 6g\times 10R}$

$\therefore \frac{v_e\left(earth\right)}{v_e\left(moon\right)}=\frac{\sqrt{60\left(2gR\right)}}{\sqrt{2gR}}=\sqrt{60}=8$