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Question

A fan is rotating with an angular speed of 150π rad/s. After switching it off, it takes 10 minutes to stop. Find the total number of revolutions made before the fan stops. (Assume constant angular retardation)

A
45000π
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B
22500π
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C
50000π
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D
22500
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Solution

The correct option is D 22500
We know, w0=150π rad/s
t=10 minutes = 10×60 s
t=600 s
we know, w=w0+αt
0=150π+α×600
α=π4 rad/s2
Using, w2w20=2αθ
02(150π)2=2×(π4)θ
θ=45000π radian
Angle covered is one revolution =2π
Number of revolutions = total angle coveredangle covered in one revolution
=45000π2π
=22500

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