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JEE Main & Advanced Physics Gravitation / गुरुत्वाकर्षण Question Bank Acceleration Due to Gravity

  • question_answer
    If earth is supposed to be a sphere of radius R, if g30 is value of acceleration due to gravity at latitude of 30o and g at the equator, the value of \[g-{{g}_{{{30}^{o}}}}\] is                 [DCE 2005]

    A)             \[\frac{1}{4}{{\omega }^{2}}R\]

    B)               \[\frac{3}{4}{{\omega }^{2}}R\]

    C)             \[{{\omega }^{2}}R\]          

    D)             \[\frac{1}{2}{{\omega }^{2}}R\]

    Correct Answer: B

    Solution :

                    Acceleration due to gravity at latitude l is given by             \[{g}'=g-R{{\omega }^{2}}{{\cos }^{2}}\lambda \] At \[{{30}^{o}},\,\,{{g}_{30{}^\circ }}=g-R{{\omega }^{2}}{{\cos }^{2}}{{30}^{o}}=g-\frac{3}{4}R{{\omega }^{2}}\] \ \[g-{{g}_{30}}=\frac{3}{4}{{\omega }^{2}}R.\]


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