Answer:
y /y₀ = 1 /√2 = 0.70
Step-by-step explanation:
To close the door, a torque must be applied in such a way that there is an angular acceleration and after a period of time the angle of the door moves.
If the force is doubled keeping the other parameters without altering angular acceleration is
F r = I α
α = F r / I
if we double the force
α = 2F r / I
α=2 α₀
let's use the angular kinematics relations
θ = w₀ t + ½ α t²
we assume the door was still before pushing it
θ = ½ a t²
t = √ (2θ / a)
as we saw the angular acceleration is double
t = √ (2θ / 2a₀)
t = 1 / √2 a₀
the relationship between the two times is
y /y₀ = 1 /√2 = 0.70
This time that has been reduced closes the door.