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JEE Main & Advanced Physics Gravitation / गुरुत्वाकर्षण Question Bank Critical Thinking

  • question_answer
    A solid sphere of uniform density and radius 4 units is located with its centre at the origin O of coordinates. Two spheres of equal radii 1 unit with their centres at A(? 2, 0, 0) and B(2, 0, 0) respectively are taken out of the solid leaving behind spherical cavities as shown in figure                                        [IIT 1993]

    A) The gravitational force due to this object at the origin is zero

    B)             The gravitational force at the point B (2, 0, 0) is zero

    C)             The gravitational potential is the same at all points of the circle \[{{y}^{2}}+{{z}^{2}}=36\]

    D)             The gravitational potential is the same at all points on the circle \[{{y}^{2}}+{{z}^{2}}=4\]

    Correct Answer: A

    Solution :

        Since cavities  are symmetrical w.r.t. O. So the gravitational force at the centre is zero. The radius of the circle \[{{z}^{2}}+{{y}^{2}}=36\] is 6. For all points for \[r\ge 6,\] the body behaves as if whole of the mass is concentrated at the centre. So the gravitational potential is same. Above is true for \[{{z}^{2}}+{{y}^{2}}=4\] as well.


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