A rigid body rotates about a fixed axis with variable angular velocity equal to (α–βt) at the time t where α,β are constants. The angle through which it rotates before it stops is
A
α22β
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B
α2−β22α
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C
3α22β
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D
(α−β)α2
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Solution
The correct option is Aα22β =α−βt whenitstopsω=0 ⇒t=αβ Also dθdt=α−βt ∫dθ=α∫α/β0dt−∫α/β0tdt θ=α(αβ)−β2×α2β2 =α22β