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JEE Main202311 Apr 2023Evening ShiftPhysicsGravitationActual

A space ship of mass 2 × 10 4 kg is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the space ship in the orbit to overcome the gravitational pull will be (if g = 10 m s - 2 and radius of earth = 6400 km ):

Options

  1. A11 . 2 ( 2 - 1 )   km   s - 1
  2. B8 ( 2 - 1 )   km   s - 1
  3. C7 . 9 ( 2 - 1 )   km   s - 1
  4. D7 . 4 ( 2 - 1 )   km   s - 1

Correct answer

B. 8 ( 2 - 1 )   km   s - 1

Step-by-step solution

The orbital velocity of satellite is v o r b = G M R The escape velocity is v e s c = 2 G M R Hence, the additional velocity required is Δ v = v e s c - v o r b = 2 G M R - G M R = ( 2 - 1 ) G M R = ( 2 - 1 ) g R = ( 2 - 1 ) 10 × 6400 × 10 3 = 8 ( 2 - 1 )   km   s - 1

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