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9th Class Science Gravitation and Floatation Question Bank Gravitation Summative Objective Problems

  • question_answer
    A geo-stationary satellite orbits around the earth in a circular orbit radius 36,000 km. Then, the time period of a spy satellite orbiting a few hundred km above the earth's surface \[\text{(}{{\text{R}}_{earth}}=\text{6},\text{4}00\,\,\text{km)}\] will approximately be

    A)  1/2 hr                  

    B)  1 hr  

    C)  2 hrs    

    D)  4 hrs

    Correct Answer: C

    Solution :

      \[{{T}^{2}}\propto {{R}^{3}};\]with \[{{R}_{e}}=6400\,\,km,\] \[\frac{{{T}^{2}}}{{{(24)}^{2}}}={{\left( \frac{6400}{36000} \right)}^{3}}\Rightarrow T\approx 1.7\,\,hr\] For spy satellite R is slightly greater than Re \[\Rightarrow {{T}_{s}}>T\]         \[\therefore {{T}_{s}}=2\,\,hr\]


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