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Question

A fan is rotating with angular velocity 100 revs/sec. Then it is switched off. It takes 5 minutes to stop.
(i) Find the total number of revolutions made before it stops. (Assume uniform angular retardation)
(ii) Find the value of angular retardation.
(iii) Find the average angular velocity during this interval.


A

(i) 15000 revs
(ii) 13 rev/s2
(iii) 50 revs/s

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B

(i) 1500 revs
(ii) 12 rev/s2
(iii) 50 revs/s

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C

(i) 10000 revs
(ii) 12 rev/s2
(iii) 50 revs/s

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D

(i) 12000 revs
(ii) 16 rev/s2
(iii) 75 revs/s

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Solution

The correct option is A

(i) 15000 revs
(ii) 13 rev/s2
(iii) 50 revs/s


Let α be the angular retardation.
Now, ω=ω0αt0=100×2πα(5×60)α=2π3 rad/s2=13 revs/s2
From third equation, ω2=ω202αθ
Substituting values we get, θ=30000π
Hence, number of revolutions, n=30000π2π=15000
Now, ωav×t=θωav=30000π5×60=100π rad/s=50 revs/s


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