Question

# A fan is rotating with angular velocity 100 revsec. Then it is switched off. It takes 5 minutes to stop. (i) Find the total number of revolution 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

No. of revolutions = 15000

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B

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C

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D

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Solution

## The correct option is C ωav = 100π rads ω0=ΔθΔt=100×2π=200π t = 5 min = 5 x 60 = 300s ω=ω0+αt ⇒ 0 = 100 x 2π + α (300) ⇒α=−200π300=−2π3rad/s2...............................(ii) ∴θ=ω0t+12(−23π)(3002) = 60,000π −π3× 90,000 = 60,000π – 30,000π ⇒ 30,000π radians No. of revolution = θ2π=30000π2π = 15,000 rev ................................(i) ωav=θt=30,000π300=100πrads......................(iii)

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