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Question

A rigid body rotates about a fixed axis with variable angular velocity equal to (αβt) at the time t where α,β are constants. The angle through which it rotates before it stops is
  1. α22β
  2. α2β22α
  3. (αβ)α2
  4. 3α22β


Solution

The correct option is A α22β
ω=αβt
when it stops ω=0
t=αβ
Also
dθdt=αβt
θ0dθ=αα/β0dtβα/β0tdt
θ=α(αβ)β2×α2β2
=α22β

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