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MHT CET 2021 (20 Sep, Shift 2) · Escape Velocity

Escape Velocity question from MHT CET 2021 (20 Sep, Shift 2)

Q51MHT CET 2021 · 20 SEP · SHIFT 2Medium

Escape Velocity

A body is projected from earth's surface with thrice the escape velocity from the surface of the earth. What will be its velocity when it will escape the gravitational pull?

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Answer: (c)

Energy conservation: $\tfrac12 mv^2 - \dfrac{GMm}{R} = \tfrac12 mv_\infty^2$ , i.e. $v_\infty^2 = v^2 - V_e^2$ .
$v = 3V_e \Rightarrow v_\infty^2 = 9V_e^2 - V_e^2 = 8V_e^2$
$v_\infty = 2\sqrt{2}\,V_e$
So the answer is (c) $2\sqrt{2}\,V_e$ .

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