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In the question number 66, if wheel star...

In the question number 66, if wheel starts from rest, what is the kinetic energy of the wheel when 2 m of the cord is unwound?

A

20 J

B

25 J

C

45 J

D

50 J

Text Solution

Verified by Experts

The correct Answer is:
d
Here, R=20 cm=0.2 m, M=20 kg
As `tau=FR=(25)N(0.2)m = 5Nm`
Moment of inertia of flywheel about its axis is
`I=(MR^(2))/(2) = ((20kg)(0.2m)^(2))/(2) = 0.4 kg m^(2)`
As `tau=Ialpha`
`therefore` Angular accelerations of the wheel,
`alpha=tau/I = (5Nm)/(0.4 kg m^(2))=12/5 rad s^(-2)`
Angular displacement of wheel,
`theta= ("Length of unwound string")/("Radius of the wheel")= (2m)/(0.2m)=10 rad`
Let `omega` be final angular velocity.
As `omega^(2) = omega_(0)^(2)+2alphatheta`
since, the wheel starts from rest, therefore `omega_(0)=0`
`therefore omega^(2) = 2 x (12.5 rad s^(-2))(10 rad) = 250 rad^(2)s^(-2)`
`therefore` Kinetic energy gained, `K=1/2Iomega^(2)`
`K=1/2 xx 0.4 kg m^(2) xx 250 rad^(2)s^(-2)= 50J`
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