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Question

A top is spinning in clockwise direction about a stationary axis. The angular acceleration of the top is given by α=θ, where θ is angular displacement of the body. At t=0, the angular velocity of body was 323π34 and angular position of the body is zero. The angular velocity of the body when it finishes two revolutions is

A
83π32
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B
43π32
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C
zero
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D
23π32
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Solution

The correct option is C zero
Initial angular velocity ω0=323 rad/s and
Initial angular position θ0=0 rad
Given that, β=θ (negative angular acceleration)
We know that β=ωdωdθ
ωdωdθ=θ
ωdw=θdθ
Integrating on both sides,
ωω0ωdω=θθ0θdθ
[ω22]ωω0=[23θ32]θθ0
ω2ω202=23θ32
ω2=ω2043θ32
For two revolutions, θ=4π and given ω0=323π34
ω2=323π3243(4π)32
ω2=323π32323π32
ω=0 rad/s

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