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JEE Main201910 Jan 2019Evening ShiftPhysicsGravitationActual

Two stars of masses 3 × 10 31 kg each, and at distance 2 × 10 11 m rotate in a plane about their common centre of mass O . A meteorite passes through O moving perpendicular to the stars,s rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at O is ( Take Gravitational constant G = 6.67 × 10 - 11 N m 2 kg - 2 )

Options

  1. A2.4 × 10 4 m s - 1
  2. B3.8 × 10 4 m s - 1
  3. C2.8 × 10 5 m s - 1
  4. D1.4 × 10 5 m s - 1

Correct answer

C. 2.8 × 10 5 m s - 1

Step-by-step solution

To escape, the total energy of small particle must be zero. T E = K E + U 0 = 1 2 m V 2 + - G M m d 2 × 2 ⇒ V = 8 G M d = 8 × 6.67 × 10 - 11 × 3 × 10 31 2 × 10 11 = 2.8 × 10 5 m s - 1

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