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JEE Main202131 Aug 2021Morning ShiftPhysicsGravitationActual

The masses and radii of the earth and moon are M 1 , R 1 and M 2 , R 2 respectively. Their centres are at a distance r apart. Find the minimum escape velocity for a particle of mass m to be projected from the middle of these two masses :

Options

  1. Av e = 4 G M 1 + M 2 r
  2. Bv e = 1 2 2 G M 1 + M 2 r
  3. Cv e = 1 2 4 G M 1 + M 2 r
  4. Dv e = 2 G M 1 + M 2 r

Correct answer

A. v e = 4 G M 1 + M 2 r

Step-by-step solution

On conserving mechanical energy. The initial total energy is equal to final total energy, ⇒ - G M 1 r 2 + G M 2 r 2 m + 1 2 m v e 2 = 0 ⇒ v e = 4 G M 1 + M 2 r .

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