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Question

Starting from rest, a fan takes four seconds to attain the maximum speed of 800 rpm (revolutions per minute). Assuming uniform acceleration, calculate the time taken by the fan in attaining half the maximum speed.

A
1 second
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B
4 seconds
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C
1.5 seconds
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D
2 seconds
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Solution

The correct option is D 2 seconds
Given,
At t=0, ω0= initial angular speed =0,
at t=4 sec,ω=800 rpm
α= constant (angular acceleration)
Using ω=ω0+αt
800=0+α×4 ... (1)

Let t be the time taken in attaining the speed of 400 rpm which is half the maximum.
Then, ω=ω0+αt
400=0+αt ... (2)
From eq. (1) and (2)
t=2 seconds

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