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JEE Main202429 Jan 2024Evening ShiftPhysicsGravitationActual

A planet takes 200 days to complete one revolution around the Sun. If the distance of the planet from Sun is reduced to one fourth of the original distance, how many days will it take to complete one revolution?

Options

  1. A25
  2. B50
  3. C100
  4. D20

Correct answer

A. 25

Step-by-step solution

The Law of Periods: The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit. T 2 ∝ r 3 Therefore, we can write T 1 2 r 1 3 = T 2 2 r 2 3 ⇒ ( 200 ) 2 r 3 = T 2 2 r 4 3 ⇒ 200 × 200 4 × 4 × 4 = T 2 2 ⇒ T 2 = 25 days

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