The correct option is C 12 rad/sec2
It is given that,
ω=θ2+2θ
differentiating both sides w.r.t t
dωdt=2θdθdt+2dθdt
We know that, angular acceleration is the differention of angular velocity with respect to time and angular velocity is the differential of angular displacement.
α=2θω+2ω
At θ=1 rad, ω=12+2×1=3 rad/s
So,
α=2θω+2ω
α=2×1×3+2×3
α=12 rad/s2
Hence option C is the correct answer.
(OR)
Angular acceleration α=ωdωdθ
Given ω=θ2+2θ
dωdθ=d(θ2+2θ)dθ=2θ+2
Now at θ=1,
ω|θ=1=12+2(1)=3
dωdθ|θ=1=2(1)+2=4
α=3(4)=12 rad/s2