The correct option is C 3
Let the uniform angular acceleration be α, the initial angular velocity ω0=0
We know that, the angular displacement for first two sec,
θ1=ω0t+12αt2, t=2 s
θ1=2α
let the angular velocity changes from ω0 to ω′ for the first 2 s, by the equation of motion under constant angular acceleration
ω′=ω0+αt⇒ω′=0+2α=2α
Now for the angular displacement for next time interval of 2 s
θ2=ω′t+12αt2, t=2 s
⇒θ2=4α+2α=6α
Hence the ratio,
θ2θ1=6α2α=3
(OR)
Let the uniform angular acceleration be α, the initial angular velocity ω0=0
The angular displacement for first two sec,
θ1=ω0t+12αt2, t=2 s
θ1=2α
The angular displacement for first four sec
θ1+θ2=ω0t+12αt2 , t=4
θ1+θ2=8α
θ2=6α
Hence the ratio,
θ2θ1=6α2α=3
Option C is the correct answer.