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

  • question_answer
    A uniform ring of mass m and radius r is placed directly above a uniform sphere of mass M and of equal radius. The centre of the ring is directly above the centre of the sphere at a distance \[r\sqrt{3}\] as shown in the figure. The gravitational field due to the ring at a distance \[\sqrt{3}r\]is.

    A) \[\frac{Gm}{8{{r}^{2}}}\]

    B) \[\frac{Gm}{4{{r}^{2}}}\]

    C) \[\sqrt{3}\frac{Gm}{8{{r}^{2}}}\]

    D) \[\frac{Gm}{8{{r}^{2}}\sqrt{3}}\]

    Correct Answer: C

    Solution :

    [c] The gravitational field due to the ring at a distance \[\sqrt{3}r\] is given by \[E=\frac{Gm(\sqrt{3})}{{{\left[ {{r}^{2}}+{{(\sqrt{3}r)}^{2}} \right]}^{3/2}}}\Rightarrow E=\frac{\sqrt{3}Gm}{8{{r}^{2}}}\]


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