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The escape velocities of two planets A and B are in the ratio 1:2. If the ratio of their radii respectively is 1:3, then the ratio of acceleration due to gravity of planet A to the acceleration of gravity of planet B will be

Asked in JEE Main 1st Feb 2nd Shift 2023 · Comparing planets

• (1) 3/2
• (2) 2/3
• (3) 3/4
• (4) 4/3

Step-by-step solution

Why the other options are wrong

• (1) Obtained by taking (g_A)/(g_B)=(v_A)/(v_B)·(R_B)/(R_A) without squaring the speed ratio.
• (2) No single consistent slip lands on 2/3. Flipping the radius factor gives (1/2)²×1/3=1/(12), and 2/3 is merely the reciprocal of the 3/2 in option 1, so this is a filler distractor.
• (4) Inverts the final fraction, which is what you get if you solve for (g_B)/(g_A) and forget to turn it over.

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