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NEET 2001 (AIPMT) · Escape Velocity

Escape Velocity question from NEET 2001 (AIPMT)

Q80NEET 2001 · AIPMTMedium

Escape Velocity

With what velocity should a particle be projected so that its height becomes equal to radius of earth?

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Answer: (a)

  1. Energy conservation up to h=Rh = R (distance 2R2R from centre): 12v2=GM(1R−12R)\frac{1}{2}v^2 = GM\left(\frac{1}{R} - \frac{1}{2R}\right).
  2. 12v2=GM2R⇒v2=GMR\frac{1}{2}v^2 = \frac{GM}{2R} \Rightarrow v^2 = \frac{GM}{R}.
  3. So the answer is (a) (GMR)1/2\left(\frac{GM}{R}\right)^{1/2}.
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