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AP EAMCET202318 May 2023Morning ShiftPhysicsGravitationActual

A satellite is placed in a circular orbit around the earth at an altitude of 1000 ~km . The time period of the satellite in minutes is approximately (mass of the earth =6 10²⁴ ~kg , radius of the earth =6.4 10^6 ~m , G =6.67 10⁻¹¹ Nm ^2 ~kg ⁻² )

Options

  1. A105
  2. B200
  3. C120
  4. D62

Correct answer

A. 105

Step-by-step solution

height, h =1000 ~km =10^6 ~m Radius of Earth, R =6.4 10^6 ~m Mass of Earth, M=6 10²⁴ ~kg Time period of satelite is given as aligned & T =2 r ^3 GM =2 ( R + h )^3 GM & T =2 3.14 (6.4 10^6+10^6 )^3 6.67 10⁻¹¹ 6 10²⁴ & =2 3.14 7.4 7.4 7.4 10¹⁸ 6.67 6 10¹³ & ~T =6.28 405.224 10^5 40.02 & ~T =6280 sec aligned aligned & = ( 6280 60 ) minutes & T=104.67 & T 105 minutes aligned

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