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NDA 2024
Exam
NDA
Year
2024
Subject
General Ability
Chapter
General Science

NDA 2024 · General Ability · General Science

Escape speed from the Earth is close to 11.2 km s^ -1 . On another...

Escape speed from the Earth is close to 11.2kms−111.2 \mathrm{ km} \mathrm{ s}^{-1}. On another planet whose radius is half of the Earth's radius and whose mass density is four times that of the Earth, the escape speed in km\mathrms−1\mathrm{km} \mathrms^{-1} will be close to:

Options

  1. A11.2
  2. B15.8
  3. C5.6
  4. D7.9

Correct answer

A. 11.2

Step-by-step solution

Escape velocity is given by, ⇒v=2gR⇒v=2GMR2×R=2GMR Also, v=2G×ρ×43πR2=11.2v′=2G×4ρ×43πR24=11.2\begin{array}{rlrl} \Rightarrow & v & =\sqrt{2 g \mathrm{R}} \\ \Rightarrow & v & =\sqrt{2 \frac{\mathrm{GM}}{\mathrm{R}^2} \times \mathrm{R}}=\sqrt{2 \frac{\mathrm{GM}}{\mathrm{R}}} \\ & \text{ Also, } & v & =\sqrt{2 \mathrm{G} \times \rho \times \frac{4}{3} \pi \mathrm{R}^2}=11.2 \\ & & v^{\prime} & =\sqrt{2 \mathrm{G} \times 4 \rho \times \frac{4}{3} \pi \frac{\mathrm{R}^2}{4}}=11.2 \end{array} Hence, escape velocity remains same.
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