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COMEDK2024Morning ShiftPhysicsGravitationActual

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 X to that of the earth is

Options

  1. A9 4
  2. B4 9
  3. C2 3
  4. D3 2

Correct answer

C. 2 3

Step-by-step solution

The escape velocity v_ e of a planet with mass M and radius R is given by the formula v_ e = 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 M_ E = 9M_ X and R_ E = 4R_ X . The escape velocity for Earth is v_ E = 2GM_ E R_ E = 2G(9M_ X ) 4R_ X = 9 4 2GM_ X R_ X = 3 2 v_ X , where v_ X is the escape velocity for planet X. The ratio of the escape velocity of planet X to that of the Earth is v_ X v_ E = v_ X 3 2 v_ X = 2 3 . Answer: 2 3

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