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Question

The angular displacement of a particle is given by θ=ω0t+12αt2, where ω0 and α are constant and ω0=1 rad/sec, α=1.5 rad/sec2. The angular velocity (in rad/s) at time, t=2 sec will be

A
1
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B
5
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C
3
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D
4
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Solution

The correct option is D 4
We have θ=ω0t+12αt2, we know that angular velocity is the rate of change of angular position of a rotating body.

dθdt=ω0+αt
This is angular velocity at time t. Now angular velocity at t=2 sec will be
ω=(dθdt)t=2 sec=ω0+2α

it is given that, ω0=1 rad/sec, α=1.5 rad/sec2

ω=1+2×1.5=4 rad/sec

Hence correct answer is (D)

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