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MHT CET 2023 (14 May, Shift 2) · Escape Velocity

Escape Velocity question from MHT CET 2023 (14 May, Shift 2)

Q33MHT CET 2023 · 14 MAY · SHIFT 2Medium

Escape Velocity

A body (mass $m$ ) starts its motion from rest from a point distant $R_0\ (R_0 > R)$ from the centre of the earth. The velocity acquired by the body when it reaches the surface of earth will be ( $G =$ universal constant of gravitation, $M =$ mass of earth, $R$ = radius of earth)

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Answer: (b)

Loss of PE = gain of KE: $\frac{1}{2}mv^2 = GMm\left(\frac{1}{R} - \frac{1}{R_0}\right)$ .
$v = \left[2GM\left(\frac{1}{R} - \frac{1}{R_0}\right)\right]^{1/2}$ .
So the answer is (b).

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