When a ceiling fan is switched on it starts from rest, while completing the 5th rotation it has angular velocity of 20rad/s, what will be the angular velocity of the fan while completing the 15th rotation ? (Assume uniform angular acceleration)
A
20√3rad/s
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B
10√3rad/s
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C
15√3rad/s
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D
5√3rad/s
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Solution
The correct option is A20√3rad/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=20rad/s)
⇒202=20π×α, α=20πrad/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×θ⇒ω2=2×20π×30π=1200 ω2=1200=20√3rad/s