JEE Main 2020 · 9 January · evening · Single correct · +4 / −1

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 v_A/v_B = n/4. The value of n is :

  1. (a) 1
  2. (b) 2
  3. (c) 4
  4. (d) 3
Answer and solution

Answer (c) 4

Solution

Physics sir · 3 steps

Escape velocity depends on M/R. Halving both leaves M/R, and so v, unchanged.

  1. Escape velocity. From the surface of a planet of mass M and radius R, the escape velocity is v = √(2GM/R). So v depends only on the ratio M/R.

    v_A/v_B = √((M_A/R_A)/(M_B/R_B)) = √((M/R)/((M/2)/(R/2))) = √1 = 1

  2. Match the form. The question writes the ratio as n/4. Setting n/4 = 1 gives n = 4.
  3. So. Both planets have the same escape velocity, and n = 4. That is option (c).

The idea to keep. For escape velocity, look at M/R: if mass and radius scale by the same factor, v_(esc) does not change. Surface gravity goes as M/R², so it does change.

Answer from the NTA final answer key. Solution by PrepWiser.

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Asked about 160 times in JEE Main since 2020. This question is from 2020.