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AP EAMCET20228 Jul 2022Evening ShiftPhysicsGravitationActual

The escape velocity of an object from a planet is 16 kms ⁻¹ . If the escape velocity of the object from another planet having twice the density and three times the radius of the planet is v 2 ~ms ⁻¹ , then the value of v is

Options

  1. A12
  2. B48
  3. C18
  4. D36

Correct answer

B. 48

Step-by-step solution

Escape speed is given by aligned v & = 2 G M R & = 2 G 4 3 R^3 d R = ( M=d V) . aligned v= 8 3 G R^2 d Now given for a planet (lets say A ) v₁=16= 8 3 G R^2 d and for planet B , v₂= 8 3 G (3 R)^2 2 d . aligned & v₁ v₂ = 16 v₂ = R^2 d (3 R)^2 2 d & 16 v₂ = 1 18 = 1 3 2 aligned Hence, v₂=48 2 ~m / s =v 2 ~ms ⁻¹ (given) v=48

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