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Question

A solid body starts from rest. Angular acceleration of the body spinning about a stationary axis is given by α=2cosθ (in rad/s2) where θ is the angle of rotation from initial position. Then which of the following graphs correctly represents the variation of angular velocity with respect to θ?

A
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B
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C
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D
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Solution

The correct option is A
Angular acceleration, α=2cosθ
α=ωdωdθ=2cosθ
Integrating on both sides,
ω0ωdω=2θ0cosθdθ
[ω22]ω0=[2sinθ]θ0
w=2sinθ rad/s
sinθ is positive between 0 & π. So option A is correct.

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