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MHT CET 2024 (9 May, Shift 2) · Escape Velocity

Escape Velocity question from MHT CET 2024 (9 May, Shift 2)

Q15MHT CET 2024 · 9 MAY · SHIFT 2Easy

Escape Velocity

The radius of the planet is double that of the earth, but their average densities are same. $V_p$ and $V_E$ are the escape velocities of planet and earth respectively. If $\frac{V_P}{V_E} = x$ , the value of ' $x$ ' is

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Answer: (c)

$v_e = \sqrt{\frac{2GM}{R}} = R\sqrt{\frac{8\pi G\rho}{3}}$ , so $v_e \propto R\sqrt{\rho}$
Same $\rho$ , $R_P = 2R_E \Rightarrow \frac{V_P}{V_E} = 2$
So the answer is (c) 2.

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