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COMEDK · Physics · 9. Gravitation

If the earth has a mass nine times and radius four times that of planet X, the ratio of the maximum speed required by a rocket to pull out of the gravitational force of planet \(\mathrm{X}\) to that of the earth is

  1. A \(\dfrac{9}{4}\)
  2. B \(\dfrac{4}{9}\)
  3. C \(\dfrac{2}{3}\)
  4. D \(\dfrac{3}{2}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\dfrac{2}{3}\)

Step-by-step Solution

Detailed explanation

The escape velocity \(v_{e}\) of a planet with mass \(M\) and radius \(R\) is given by the formula \(v_{e} = \sqrt{\dfrac{2GM}{R}}\). Let \(M_{E}\) and \(R_{E}\) be the mass and radius of the Earth, and \(M_{X}\) and \(R_{X}\) be the mass and radius of planet X. Given…