Gravitation - Result Question 39
42. The radius of a planet is twice the radius of earth. Both have almost equal average massdensities. If $V_P$ and $V_E$ are escape velocities of the planet and the earth, respectively, then
[NEET Kar. 2013]
(a) $V_E=1.5 V_P$
(c) $V_P=2 V_E$
(b) $V_P=1.5 V_E$
(d) $V_E=3 V_P$
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Answer:
Correct Answer: 42. (c)
Solution:
- (c) Escape velocity,
$ \begin{aligned} V_e & =\sqrt{\frac{2 G M_E}{R_E}}=\sqrt{\frac{2 G}{R_E}(\frac{4}{3} \pi R_E^{3} \rho_E)}=R \sqrt{\frac{8}{3} \pi G \rho_E} \\ & \Rightarrow V_e \propto R \Rightarrow \frac{V_P}{V_E}=\frac{R_P}{R_E}=2 \\ & \Rightarrow V_P=2 V_E . \end{aligned} $
