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Question: Answered & Verified by Expert
There are two planets and the ratio of radius of the two planets is $K$ but ratio of acceleration due to gravity of both planets is $g$. What will be the ratio of their escape velocity?
PhysicsGravitationJIPMERJIPMER 2006
Options:
  • A $(K g)^{1 / 2}$
  • B $(K g)^{-1 / 2}$
  • C $(K g)^2$
  • D $(\mathrm{Kg})^{-2}$
Solution:
2458 Upvotes Verified Answer
The correct answer is: $(K g)^{1 / 2}$
$\begin{aligned} v_e & =\sqrt{R g} \\ \frac{v_1}{v_2} & =\sqrt{\frac{R_1}{R_2} \cdot \frac{g_1}{g_2}} \\ & =\sqrt{K g} \\ & =(K g)^{1 / 2}\end{aligned}$

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