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The escape velocity of a body on a planet A is 12 km s⁻¹. The escape velocity of the body on another planet B, whose density is four times and radius is half of the planet A, is

Asked in JEE Main 29th June 1st Shift 2022 · Comparing planets

• (1) 12 km s⁻¹
• (2) 24 km s⁻¹
• (3) 36 km s⁻¹
• (4) 6 km s⁻¹

Step-by-step solution

Why the other options are wrong

• (2) Uses √ρ=2 and forgets that halving the radius pulls the escape speed back down by the same factor.
• (3) Comes from multiplying the density factor 4 by a stray √R term instead of using vₑ∝ R√ρ.
• (4) Applies the radius factor 1/2 alone and drops the density change.

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