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Question

When a ceiling fan is switched on it starts from rest, while completing the 5th rotation it has angular velocity of 20 rad/s, what will be the angular velocity of the fan while completing the 15th rotation ? (Assume uniform angular acceleration)

A
203 rad/s
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B
103 rad/s
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C
153 rad/s
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D
53 rad/s
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Solution

The correct option is A 203 rad/s
We know that, by the equation of motion under constant angular acceleration,

ω2=ω20+2αθ,
θ=2πn=2π(5)=10π where n is the number of rotation and is given that it starts from rest so, ω0=0

we get,
ω2=2α×θ=2α×10π
after 5 revolutions it is given that angular velocity becomes (ω=20 rad/s)

202=20π×α, α=20π rad/s2
The angular displacement of the fan while completing the 15th rotation will be θ=2π×n=2π×15=30π radian

By the equation of motion under constant angular acceleration we get,
ω2=2α×θω2=2×20π×30π=1200
ω2=1200=203 rad/s

Hence option A is the correct answer.

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