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A wheel of moment of inertia 2 kgm^(2) ...

A wheel of moment of inertia `2 kgm^(2)` is rotating about an axis passing through centre and perpendicular to its plane at a speed `60 rad//s`. Due to friction, it comes to rest in 5 minutes. The angular momentum of the wheel three minutes before it stops rotating is

A

`"24 kg m"^(2)//s`

B

`"48 kg m"^(2)//s`

C

`"72 kg m"^(2)//s`

D

`"96 kg m"^(2)//s`

Text Solution

Verified by Experts

The correct Answer is:
C
Angular acceleration (a) of the wheel is
`alpha=(w-w_(0))/(t)=(0-60)/(5xx60)=-(1)/(5)" rad/s"^(2)`
and `w=w_(0)+alphat`
The wheel stops after 5 minutes.
`therefore` 3 minutes before it stops rotating means 2 minutes, ater starting from rest.
`therefore w=w_(0)+alphaxx2=60-(1)/(5)xx2xx60`
`=60-24="36 rad/s"`
`therefore` Angular momentum `=Iomega`
`=2xx36="72 kg m"^(2)//s" ...Option(c)"`
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