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MHT CET 2022 (11 Aug, Shift 2) · Escape Velocity

Escape Velocity question from MHT CET 2022 (11 Aug, Shift 2)

Q42MHT CET 2022 · 11 AUG · SHIFT 2Difficult

Escape Velocity

The masses and radii of the moon and the earth are M1,R1M_1, R_1 and M2,R2M_2, R_2 respectively. Their centres are at a distance dd apart. What should be the minimum speed with which a body of mass 'mm' should be projected from a point midway between their centres, so as to escape to infinity?

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Answer: (b)

  1. At the midpoint each mass is d/2d/2 away: V=−2GM1d−2GM2d=−2G(M1+M2)dV = -\dfrac{2GM_1}{d} - \dfrac{2GM_2}{d} = -\dfrac{2G(M_1+M_2)}{d}.
  2. 12mv2=m∣V∣⇒v2=4G(M1+M2)d\tfrac12 mv^2 = m|V| \Rightarrow v^2 = \dfrac{4G(M_1+M_2)}{d}
  3. v=2G(M1+M2)dv = 2\sqrt{\dfrac{G(M_1+M_2)}{d}}
  4. So the answer is (b).
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