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The earth has 8 times the mass and 2 times the radius of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity from the planet in km/s will be

Asked in JEE Main 28th Jan 2nd Shift 2025 · Comparing planets

• (1) 11.2
• (2) 8.4
• (3) 5.6
• (4) 2.8

Step-by-step solution

Why the other options are wrong

• (1) Assumes the two factors cancel outright, treating M/R as unchanged when it is really quartered.
• (2) Three quarters of the earth's value, which appears if the ratio is built as 1-1/8×2 style arithmetic instead of √(Mₚ Rₑ)/(Mₑ Rₚ).
• (4) Divides by four instead of two, that is, uses M/R=1/4 directly as the speed ratio and forgets the square root.

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