Q130 / 160 · AP EAMCET 2004 · Physics

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 :

  • A
    $0$
  • B
    $v_e$
  • C
    $\sqrt{2} v_e$
  • Correct answer
    D
    $2v_e$

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 $$ \begin{aligned} v^{\prime} & =\sqrt{v^2-v_e^2} \\ \therefore \quad v^{\prime} & =\sqrt{\left(\sqrt{5} v_e\right)^2-v_e^2}=2 v_e \end{aligned} $$

Hence, the correct answer is option: 'D'.

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