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JEE Main & Advanced Physics Gravitation / गुरुत्वाकर्षण Question Bank Self Evaluation Test - Gravitation

  • question_answer
    If the radius of the earth were to shrink by 1 %, with its mass remaining the same, the acceleration due to gravity on the earth's surface would

    A) Decrease by 1%

    B) decrease by 2%

    C) Increase by 1%

    D) increase by 2%

    Correct Answer: D

    Solution :

    [d] As \[g=\frac{GM}{{{R}^{2}}}\] when radius is reduced by 1% then \[R'=R-\frac{R}{100}=.99R,\] so \[\operatorname{g}'=\frac{GM}{{{(.99R)}^{2}}}=1.02\frac{GM}{{{R}^{2}}}\] \[\Rightarrow \text{ }%\text{ }increase\text{ }=2%\]


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