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

  • question_answer
    Let g be the acceleration due to gravity at earth's surface and K be the rotational kinetic energy of the earth. Suppose the earth's radius decreases by 2% keeping all other quantities same, then [BHU 1994; JIPMER 2000]

    A) g decreases by 2% and K decreases by 4%

    B)             g decreases by 4% and K increases by 2%

    C)             g increases by 4% and K increases by 4%

    D)             g decreases by 4% and K increases by 4%

    Correct Answer: C

    Solution :

        \[g=\frac{GM}{{{R}^{2}}}\]and \[K=\frac{{{L}^{2}}}{2I}\] If mass of the earth and its angular momentum remains constant then \[g\propto \frac{1}{{{R}^{2}}}\] and \[K\propto \frac{1}{{{R}^{2}}}\] i.e. if radius of earth decreases by 2% then g and K both increases by 4%.


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