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JEE Main202310 Apr 2023Evening ShiftPhysicsGravitationActual

The time period of a satellite, revolving above earth's surface at a height equal to R will be (Given g = π 2 m s - 2 , R = radius of earth)

Options

  1. A2 R
  2. B8 R
  3. C32 R
  4. D4 R

Correct answer

C. 32 R

Step-by-step solution

The velocity of the satellite revolving round the Earth at a height r from the centre of the Earth is given by v = G M r       . . . 1 The formula to calculate the time period in the circular orbit is given by T = 2 π r v       . . . 2 In this case: r = R + R = 2 R Substitute the expression for the velocity from equation (1) into equation (2) and simplify to obtain the required time period. T = 2 π r GM r = 2 π × 2 R g R 2 = 4 π R 2 π R = 4 2 R = 32 R

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