Looking for classes? Ksquare Career Institute, Bengaluru →
The escape velocity for earth is $v$. A planet having 9 times mass that of earth and radius, 16 times that of earth, has the escape velocity of:
A
$3v$
B
$\dfrac{2}{3}v$
C
$\dfrac{3}{4}v$
D
$\dfrac{9}{4}v$
Detailed Solution
$V_e=\sqrt{\dfrac{2GM}{R}}\propto\sqrt{\dfrac{M}{R}}$. $\dfrac{(V_e)_p}{(V_e)_e}=\sqrt{\dfrac{M_p}{M_e}\times\dfrac{R_e}{R_p}}=\sqrt{\dfrac{9}{16}}=\dfrac{3}{4}$, so $(V_e)_p=\dfrac{3}{4}v$.