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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. 3α22β
  3. α2β22α
  4. (αβ)α2


Solution

The correct option is A α22β
=αβt
when it stops ω=0
t=αβ
Also
dθdt=αβt
dθ=αα/β0dtα/β0tdt
θ=α(αβ)β2×α2β2
=α22β

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