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Question

A disc which is at rest started to spin about a stationary axis. The angular acceleration of the disc is given by α=2θ rad/s, where θ is the angle of rotation of disc from its initial position. 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 B
Given α=2θ
We know α=dωdt=dωdθ×dθdt
ωdωdθ=2θ
ωdω=2θdθ
Integrating on both sides,
ω0ωdω=θ02θdθ
ω22=2θ22
w=2θ
Therefore, graph is a straight line passing through origin. (option b)

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