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A satellite is orbiting just above the surface of the earth with period T . If d is the density of the earth and G is the universal constant of gravitation, the quantity 3 π G d represents :

Options

  1. AT
  2. BT
  3. CT 2
  4. DT 3

Correct answer

C. T 2

Step-by-step solution

The formula to calculate the mass of the Earth considering it a sphere is given by M = 4 3 π R 3 d . . . 1 The formula to calculate the time period of revolution of the satellite can be written as T = 2 π R 3 G M . . . 2 Substitute the expression for the mass from equation (1) into equation (2) and simplify to obtain the expression for the required quantity. T = 2 π R 3 G 4 3 π R 3 d = 2 π 3 4 π G d = 12 π 2 4 π G d = 3 π G d ⇒ 3 π G d = T 2

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