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NTA Abhyas JEE Main2020PhysicsGravitationPractice

A planet revolves about the sun in an elliptical orbit of semi-major axis 2 × 10 12 m . The areal velocity of the planet when it is nearest to the sun is 4 .4 × 10 16 m 2 s - 1 . If the least distance between the planet and the sun is 1 .8 × 10 12 m , then the minimum speed of the planet is

Options

  1. Av min = 40   km   s - 1
  2. Bv min = 30   km   s - 1
  3. Cv min = 10   km   s - 1
  4. Dv min = 20   km   s - 1

Correct answer

A. v min = 40   km   s - 1

Step-by-step solution

The areal velocity of a planet around the sun is d A d t = L 2 m , where L is the angular momentum of the planet around the sun and m is its mass. 4 . 4 × 10 16 = m v min r max 2 m 2 × 4 . 4 × 10 16 = v min 4 × 10 12 - 1 . 8 × 10 12 v min = 40   km   s - 1

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