A spherical ball rolls on a table without slipping. Determine the percentage of its `K.E.` which is rotational. Moment of inertia of sphere `= (2//5) xx mass xx ("radius")^(2)`.

Options

A. `50%`
B. `40%`
C. `70%`
D. `90%`

Explanation

K.E of rotation `=1/2 I omega ^(2) = (1)/(2) I xx (v ^(2))/( r ^(2))`
`= (1)/(2) xx (2)/(3) xx ( m xx r ^(2) xx v ^(2))/( r ^(2))`
K.E. of rotation `= 1/3 mv ^(2)`
Thtal energy `= (1)/(2) mv ^(2) (1 + (K ^(2))/( R ^(2))) = (1)/(2) mv ^(2) (1 + (2)/(3))`
`= (5)/(6) mv ^(2)`
`therefore ("Rotational K.E")/("Totla Energy") xx 100= ((1)/(3) mv ^(2))/( (5)/(6) mv ^(2))xx 100%`