The escape velocity of a body on the earth surface is $11.2 \mathrm{~km} / \mathrm{s}$. If the same body is…

The escape velocity of a body on the earth surface is $11.2 \mathrm{~km} / \mathrm{s}$. If the same body is projected upward with velocity $22.4 \mathrm{~km} / \mathrm{s}$, the velocity of this body at infinite distance from the centre of the earth will be
  1. $11.2 \mathrm{~km} / \mathrm{s}$
  2. $11.2 \sqrt{3} \mathrm{~km} / \mathrm{s}$
  3. $11.2 \sqrt{2} \mathrm{~km} / \mathrm{s}$
  4. Zero

Solution

$\begin{aligned} & V^{\prime 2}=V^2-V e^2 \\ & V^{\prime}=\sqrt{V^2-V e^2} \\ & =\sqrt{(22.4)^2-(11.2)^2} \\ & V^{\prime}=11.2 \sqrt{3} \mathrm{~km} / \mathrm{s}\end{aligned}$

Asked in: NEET 2023 (Manipur)

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