A small sphere I of radius r and mass m rolls without slipping inside a large hemispherical bowl of radius R as shown in figure. The sphere I starts from rest at the top point on the rim of the hemisphere. Find the normal force exerted by small sphere on the hemisphere when it touches the bottom of hemisphere.

A small sphere I of radius r and mass m rolls without slipping inside a large hemispherical bowl of radius R as shown in figure. The sphere I starts from rest at the top point on the rim of the hemisphere. Find the normal force exerted by small sphere on the hemisphere when it touches the bottom of hemisphere.

  1. A

    10mg7

  2. B

    9mg7

  3. C

    17mg7

  4. D

    3mg7

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    Solution:

    Velocity on reaching the bottom:

    mg(R-r) = 710mv2

    v2= 107g(R-r)

    N-mg = mv2R-r     N= 177mg

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