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JEE Main202312 Apr 2023Morning ShiftPhysicsGravitationActual

The ratio of escape velocity of a planet to the escape velocity of earth will be:- Given: Mass of the planet is 16 times mass of earth and radius of the planet is 4 times the radius of earth.

Options

  1. A4   :   1
  2. B1   :   4
  3. C1   :   2
  4. D2   :   1

Correct answer

D. 2   :   1

Step-by-step solution

The formula to calculate the escape velocity is given by v e = 2 G M R       . . . 1 For the Earth, it is given by v e E = 2 G M E R E . . . 2 and, for the planet, it is given by v e P = 2 G M P R P . . . 3 Divide equation (2) by equation (3) and simplify to obtain the required ratio. v e E v e P = M E M P × R P R E       . . . 4 Substitute the values of the known parameters into equation (4) to obtain the required ratio. v e E v e P = M E 16 M E × 4 R E R E = 1 2 ⇒ v e

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