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A wheel is rotating freely at an angular...

A wheel is rotating freely at an angular speed of 800 rev/min on a shaft whose rotational inertia is negligible. A second wheel initially at rest with thrice the rotational inertia of the first is suddenly coupled to the same shaft. The fraction of original kinetic energy lost is

A

`(5)/(6)`

B

`(1)/(4)`

C

0

D

`(3)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
D
From angular momentum conservation :
`I omega+0=I omega_(C)+3Iomega_(C)`
`omega_(C)=(omega)/(4)`
Loss of kinetic energy = `(1)/(2)I omega^(2)-(1)/(2)(I+3I)((omega)/(4))^(2)`
= `(1)/(2)I omega^(2)-(1)/(2)I(omega^(2))/(4)`
= `(3)/(8) I omega^(2)`
Fractional loss = `(3)/(4)`
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