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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=ω0−αt⇒0=100×2π−α(5×60)⇒α=2π3 rad/s2=13 revs/s2 From third equation, ω2=ω20−2αθ 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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