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Question

A point on the rim of a disc starts circular motion from rest and after time t, it gains an angular acceleration given by α=3tt2. The angular velocity after 2 sec is:

A
53 rad/s
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B
103 rad/s
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C
54 rad/s
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D
52 rad/s
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Solution

The correct option is B 103 rad/s
Angular acceleration is the rate of change of angular velocity w.r.t time.

α=dωdt

dω=αdt

dω=(3tt2)dt

Putting the limits of time from t=0 to t=2 sec.

ω=dω=20(3tt2)dt

ω=[3t22]20[t33]20

ω=3[20][83]

ω=683=103 rad/s

Hence, option (b) is correct.
Why this Question?
Caution: The kinetic equation can be used only when α is constant, in problems involving variable ω or α, we have to use the basic definition of α or ω and solve it using differentiation or integration (as applicable).

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