A small solid sphere of mass m and radius r rolls without slipping on the inside a large hemisphere of radius R . The axis of symmetry of the hemisphere is vertical. Sphere starts at the top from rest. The sphere will exert a normal force on the hemisphere at its bottom equal to (n)17/14mg. Then the value of n is..

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Elizabeth Oneill · Accepted Answer

K.E  of sphere at the bottom   1      /    2  m      v    2    c  m  +  1      /    2  I  c  m            ω        2    =  1      /    2  m      v    2    c  m  +  1      /    2  ⋆  2      /    5  m      r    2    (  v  c  m      /    r      )    2      1      /    2  m      v    2    c  m  +  1      /    5  m      v    2    c  m  =  7      /    10  m      v    2    c  m KE of sphere at bottom   =  7      /    10  m      v    2    c  m  =  m  g  R Centrifugal force   =  m      v    2    c  m      /    R  =  m  g  ∗  10      /    7  N  −      F          c      e      n      t      r      i      f      u      g      a      l        =  m  g    ⟹  m  g  +  m                    v        2            c      m        R    =  N  =      17    7    m  g    n  =  2

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