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JEE Main2016PhysicsGravitationActual

The figure shows an elliptical path A B C D of a planet around the sun S such that the area of triangle C S A is 1 4 the area of the ellipse. (see figure) with D B as the major axis, and C A as the minor axis. If t 1 is the time taken for the planet to go over path A B C and t 2 for path taken over C D A then:

Options

  1. At 1 = 4 t 2
  2. Bt 1 = 2 t 2
  3. Ct 1 = 3 t 2
  4. Dt 1 = t 2

Correct answer

C. t 1 = 3 t 2

Step-by-step solution

Using Kepler's law, Area A B C D A = x . Area S A B C S = x 4 + x 2 = 3 x 4 . Area S A D C S = x 2 - x 4 = x 4 . Since Arial velocity remains constant. Therefore, area swept will be proportional to time. 3 x 4 x 4 = t 1 t 2 ⇒ t 1 = 3 t 2

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