A disc roll on an inclined plane without slipping Rotational and total energy is

Options

A. `3:1`
B. `1:3`
C. `sqrt3:1`
D. `0:1`

Explanation

Total kinetic energy `= (1)/(2) mv ^(2) (1 + (K ^(2))/( R ^(2)))...a .`
Rotational kinetic energy `= (1)/(2) mv ^(2) ((K ^(2))/( R ^(2))) ...b.`
from eq. a and b. we get
`therefore (E _(r))/( E_(R)) = ((1)/(2) mv ^(2) (1 + (K ^(2))/(R^(2))))/((1)/(2) mv ^(2) ((K ^(2))/( R ^(2)))) = (1 + (K ^(2))/( R ^(2)))/(( K ^(2))/( R ^(2)))`
`= (1 + (1)/(2))/( (1)/(2)) = 3 ` (for disc `(K _(2))/( R ^(2)) = (1)/(2))`
`= 2/5 xx 100%`
`= 40%`