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The escape velocity for earth is \(v\). A planet having 9 times mass that of earth and radius, 16 times that of earth, h…

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The escape velocity for earth is \(v\). A planet having 9 times mass that of earth and radius, 16 times that of earth, has the escape velocity of:

[Re-NEET 2024]

a

\(\frac{v}{3}\)

b

\(\frac{2v}{3}\)

c

\(\frac{3v}{4}\)

d

\(\frac{9v}{4}\)

✓ Correct answer: c)

\(\frac{3v}{4}\)

Explanation

Escape velocity v = √(2GM/R).

Earth: v = √(2GMₑ/Rₑ)

Planet: M' = 9Mₑ, R' = 16Rₑ.

v' = √(2G(9Mₑ)/(16Rₑ)) = √(9/16) * √(2GMₑ/Rₑ) = (3/4)v

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