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JEE Main & Advanced Sample Paper JEE Main Sample Paper-17

  • question_answer
    A spherical cavity is made in solid sphere of radius R. The mass of the sphere before the cavity was eked out was M. The gravitational field intensity at the center of the sphere due  to remaining mass is

    A)  Zero                     

    B)  \[\frac{GM}{8{{R}^{2}}}\]

    C)  \[\frac{GM}{2{{R}^{2}}}\]                           

    D)  \[\frac{GM}{{{R}^{2}}}\]

    Correct Answer: C

    Solution :

     Mass of cavity (i.e., of the portion removed), \[M=\rho \times \frac{4}{3}\pi \frac{{{R}^{3}}}{8}=\frac{M}{8}\]                 So,          \[{{\vec{E}}_{\text{resultant}}}={{\vec{E}}_{M}}-{{\vec{E}}_{M/8}}\]                                 \[=0-\frac{G(M/8)}{{{(R/2)}^{2}}}=\frac{-GM}{2{{R}^{2}}}\] \[-\text{ve}\]sign gives the direction i.e., it is away from the centre of cavity.


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