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JEE Main202324 Jan 2023Evening ShiftPhysicsGravitationActual

If the distance of the earth from Sun is 1 . 5 × 10 6 km , then the distance of an imaginary planet from Sun, if its period of revolution is 2 . 83 years is:

Options

  1. A  6   ×   10 7   km
  2. B  6   ×   10 6   km
  3. C3   ×   10 6   km
  4. D3   ×   10 7   km

Correct answer

C. 3   ×   10 6   km

Step-by-step solution

From Kepler's law of periods, we know that T 2 ∝ R 3 ⇒ T 1 T 2 2 = R 1 R 2 3 ⇒ 1 2 . 83 2 = 1 . 5 × 10 6 R 2 3 ⇒ R 2 = 2 . 83 2 × 1 . 5 × 10 6 3 1 3 = 8 1 3 × 1 . 5 × 10 6 = 3 × 10 6   km

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