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JEE Main20231 Feb 2023Morning ShiftPhysicsGravitationActual

If earth has a mass nine times and radius twice to the of a planet P . Then v e 3 x m s - 1 will be the minimum velocity required by a rocket to pull out of gravitational force of P , where ve is escape velocity on earth. The value of x is

Options

  1. A2
  2. B3
  3. C18
  4. D1

Correct answer

A. 2

Step-by-step solution

The formula to calculate the escape velocity v e for the Earth is given by v e =   2 G M e R e . . . . . . . . . . . . . . . . . . . . . . . ( 1 ) where, G is the Universal Gravitational constant, M e is the mass and R e is the radius of Earth. The formula for the escape velocity v esc of any planet is given by v esc =   2 G M R . . . . . . . . . . . . . . . . . . . . . . . . ( 2 ) where, M is the mass and R is the radius of the planet. Given that the mass of the planet is 9 times the mass of the Earth an

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