The escape velocity of a body on the earth's surface is $v_e$.A body is thrown up with a speed $\sqrt{5}…

The escape velocity of a body on the earth's surface is $v_e$.A body is thrown up with a speed $\sqrt{5} v_e$.Assuming that the sun and planets do not influence the motion of the body, velocity of the body at infinite distance, is :
  1. $0$
  2. $v_e$
  3. $\sqrt{2} v_e$
  4. $2v_e$

Solution

Since velocity of projection $(v)$ is greater than the escape velocity $\left(v_e\right)$, therefore at infinite distance the body moves with a velocity $ \begin{aligned} v^{\prime} & =\sqrt{v^2-v_e^2} \\ \therefore \quad v^{\prime} & =\sqrt{\left(\sqrt{5} v_e\right)^2-v_e^2}=2 v_e \end{aligned} $

Asked in: AP EAMCET 2004

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