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JEE Main & Advanced Physics Gravitation / गुरुत्वाकर्षण Question Bank Mock Test - Gravitation and Mechanical Properties of Solid

  • question_answer
     A satellite moves eastwards very near the surface of the Earth in equatorial plane with speed (\[{{v}_{0}}\]). Another satellite moves at the same height with the same speed in the equatorial plane but westwards. If \[R\]= radius of the Earth and \[\omega \]) be its angular speed of the Earth about its own axis. Then find the approximate difference in the two time period as observed on the Earth.

    A) \[\frac{4\pi \omega {{R}^{2}}}{{{v}_{0}}^{2}+{{R}^{2}}{{\omega }^{2}}}\]       

    B) \[\frac{2\pi \omega {{R}^{2}}}{{{v}_{0}}^{2}-{{R}^{2}}{{\omega }^{2}}}\]

    C) \[\frac{4\pi \omega {{R}^{2}}}{{{v}_{0}}^{2}-{{R}^{2}}{{\omega }^{2}}}\]        

    D) \[\frac{2\pi \omega {{R}^{2}}}{{{v}_{0}}^{2}+{{R}^{2}}{{\omega }^{2}}}\]

    Correct Answer: C

    Solution :

    [c] \[{{T}_{west}}=\frac{2\pi R}{{{v}_{0}}+R\omega }\] and \[{{T}_{east}}=\frac{2\pi R}{{{v}_{0}}-R\omega }\Rightarrow \Delta T={{T}_{east}}\] \[\Rightarrow {{T}_{east}}-{{T}_{west}}=2\pi R\left[ \frac{2\pi R}{{{v}^{2}}_{0}-{{R}^{2}}{{\omega }^{2}}} \right]=\frac{4\pi \omega {{R}^{2}}}{{{v}_{0}}^{2}-{{R}^{2}}{{\omega }^{2}}}\]


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