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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 37

  • question_answer
    A satellite moves round the earth in a circular orbit of radius R making one revolution per day. A second satellite moving in a circular orbit, moves round the earth once in 8 days. The radius of the orbit of the second satellite is

    A) 8 R                              

    B) 4 R     

    C) 2 R                  

    D)        R

    Correct Answer: B

    Solution :

    As, \[{{\operatorname{T}}^{2}}\,\,\propto \,\,{{R}^{3}}\] \[\therefore \,\,\,\,\frac{T_{A}^{2}}{T_{B}^{2}}=\frac{{{R}_{{{A}^{3}}}}}{{{R}_{{{B}^{3}}}}}\] \[{{\left( \frac{T_{A}^{{}}}{8T_{B}^{{}}} \right)}^{2}}\,\,=\,\,{{\left( \frac{{{R}_{{{A}^{{}}}}}}{{{R}_{{{B}^{{}}}}}} \right)}^{3}}\,\,\,\,\,\,\,\,\,\,\,\,[\because \,\,{{T}_{B}}=8{{T}_{A}}]\] \[{{\left( \frac{1}{8} \right)}^{2}}={{\left( \frac{{{R}_{A}}}{{{R}_{B}}} \right)}^{3}}\] \[\Rightarrow \,\,\,\frac{1}{64}={{\left( \frac{{{R}_{A}}}{{{R}_{B}}} \right)}^{3}}\] \[\Rightarrow \,\,\,{{\left( \frac{1}{4} \right)}^{3}}\,\,=\,\,{{\left( \frac{{{R}_{A}}}{{{R}_{B}}} \right)}^{3}}\] \[\Rightarrow \,\,\,{{\left( \frac{1}{4} \right)}^{3}}={{\left( \frac{{{R}_{A}}}{{{R}_{B}}} \right)}^{3}}\] \[\Rightarrow \,\,\,\frac{1}{4}=\,\,\frac{{{R}_{A}}}{{{R}_{B}}}\] \[\Rightarrow \,\,\,{{\operatorname{R}}_{B}}=4{{R}_{A}}=4R\]


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