Question 21: Gravitation

Question

A planet is 121 times heavier than moon and has a diameter 9 times that of moon. If the escape velocity on the planet is $v$, then the escape velocity on the moon will be:

Accepted Answer

We use the fact that
$$v_e=\sqrt{\frac{2GM}{R}}\,. $$
Let the planetÃ¢ÂÂs escape speed be $v_p=v$. Then for the moon:
$ v_m =\sqrt{\frac{2G\,M_m}{R_m}} =\sqrt{\frac{2G\,(M_p/121)}{(R_p/9)}} =v\sqrt{\frac{9}{121}} =\frac{3}{11}\,v. $
Answer: $\displaystyle \frac{3v}{11}$ (Option D).

Answer

$\frac{11 v}{3}$

Answer

$\frac{33 v}{8}$

Answer

$\frac{8 v}{33}$

Answer

$\frac{3 v}{11}$

Gravitation

A planet is 121 times heavier than moon and has a diameter 9 times that of moon. If the escape velocity on the planet is v, then the escape velocity on the moon will be:

Choose the correct answer: