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JEE Main201912 Apr 2019Evening ShiftPhysicsGravitationActual

The ratio of the weights of a body on Earth’s surface to that on the surface of a planet is 9 : 4 The mass of the planet is 1 9 t h of that of the Earth. If R is the radius of the Earth, what is the radius of the planet? (Take the planets to have the same mass density)

Options

  1. AR 4
  2. BR 2
  3. CR 3
  4. DR 9

Correct answer

B. R 2

Step-by-step solution

Weight = m G M R 2 ∴ 9 4 = G M e R e 2 × R p 2 G M p Given that, M p = M e 9 ∴ 9 4 = M e M e 9 × R p 2 R e 2 R p 2 = R e 2 × 1 4 R p = R e 2 As, R e = R ⇒ R p = R 2

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