1.

A wheel of mass `5 kg` and radius `0.40 m` is rolling on a road without sliding with angular velocity `10 rad s^-1`. The moment of ineria of the wheel about the axis of rotation is `0.65 kg m^2`. The percentage of kinetic energy of rotate in the total kinetic energy of the wheel is.A. `22.4 %`B. `11.2 %`C. `88.8 %`D. `44. 8 %`

Answer» Correct Answer - D
(d) Here, `m = 5kg, I = 0.65 kg m^2`
`omega = 10 rad s^-1, R = 0.40 m`
Linear velocity
`v = R omega = 0.40 xx 10 = 4 m s^-1`
Translation `KE`
=`(1)/(2) mv^2 = (1)/(2) xx 5 xx 16 = 40 J`
Rotational `KE`
=`(1)/(2) I omega^2 = (1)/(2) xx 0.65 xx 100 = 32.5 J`
Total `KE` = Translational `KE + Rotational KE`
=`40 + 32.5 = 72.5 J`
percentage of rotational `KE = (Rotational KE)/(Total KE) xx 100`
=`(32.5)/(72.5) xx 100 = 44.8 %`.


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