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A wheel of mass 5 kg and radius 0.40 m i...

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 inertia 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%`

Text Solution

Verified by Experts

The correct Answer is:
D
Here , m=5 kg, I=0.65 kg `m^(2)`
`omega = 10 rad s^(-1), R=0.40 m`
Linear velocity
`v=Romega = 0.40 xx 10 = 4 ms^(-1)`
Translation KE = `1/2mv^(2) = 1/2 xx 5 xx 16= 40 `J
Rotational KE `=1/2omega^(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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