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Question

When a ceiling fan is switched on, it makes 10 revolutions in the first 3 seconds. Assuming a uniform angular acceleration, how many rotations it will make in the next 3 seconds?

A
10
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B
20
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C
30
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D
40
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Solution

The correct option is C 30
According to the question

Ceiling fan makes 10 revolutions in the first 3 seconds
θ1=2π×10=20π radian

Using equation of motion for circular motion
Using θ=ω0t+12αt2
20π=12α×3×3α=40π9rad s2

Now,
Angular velocity at the end of 3 s

ω1=ω0+αt=0+40π9×3=40π3rad s1
If θ2 represents the angular displacement from 3 s to 6s, then
θ2=ω1t+12αt2=40π3×3+12×40π9×9=60π
Number of rotations =60π2π=30.

Hence the number of rotations is 30.


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