CBSE Class 11-science Answered

When a ball rolls down without slipping , it possesses both rotational K.E. and translational K.E. Total K.E. of solid ball

K = K _r + K_t

or, K = (Iω ² / 2)  +  ( mv² /2)

         = (1/2) ( 2MR² / 5 ) ω ²  + ( mv² /2)

         =  ( 1/5) MR² ω ²   + ( mv² /2)

         = ( 1/5)mv²  + ( mv² /2)

or, K = ( 7/10)  mv²

Rotational K.E. =  (1/5)mv² 

Total K.E.    =   ( 7/10)  mv²

Fractional rotatinal K.E.  = (1/5)mv²  /  ( 7/10)  mv²

                                              =  2/7