JEE PYQ: Gravitation Question 33
Question 33 - 2020 (09 Jan Shift 2)
Planet A has mass $M$ and radius $R$. Planet B has half the mass and half the radius of Planet A. If the escape velocities from the Planets A and B are $v_A$ and $v_B$, respectively, then $\frac{v_A}{v_B} = \frac{n}{4}$. The value of $n$ is:
(1) 4
(2) 1
(3) 2
(4) 3
Show Answer
Answer: (1)
Solution
$v_e = \sqrt{\frac{2GM}{R}}$. $v_A = \sqrt{\frac{2GM}{R}}$, $v_B = \sqrt{\frac{2G(M/2)}{R/2}} = \sqrt{\frac{2GM}{R}} = v_A$. So $\frac{v_A}{v_B} = 1 = \frac{n}{4}$, giving $n = 4$.
BETA
