Physics question below?

Question

Two thin rectangular sheets (0.06 m* 0.46 m) are identical. In the first sheet the axis of rotation lies along the 0.06 m side, and in the second it lies along the 0.46 m side. The same torque is applied to each sheet. The first sheet, starting from rest, reaches its final angular velocity in 7.4 s. How long does it take for the second sheet, starting from rest, to reach the same angular velocity?

Answer 1

Let the two case be identified as having moment-of-inertia I1 and I2.
Torque T on to the each of the two bodies produces angular accelerations (alfa1 and alfa2) given by the relation T= I x alpha

alfa1 = T/ I1 and alfa2 = T/I2

Starting form rest(wi =0), let the time taken to reach final angular velocity wf be t1
using: wf =- wi + alfa x t

wf/alfa1 = t1 and wf/alfa2 = t2
leading to

t2 = alfa1x t1/alfa2

= I2 xt1/I1
= (I2/I1) x t1
=. ......Ans
(Hoping you will put the values and get the answer you want)

Answer 2

αωθ
τ = Iα
α = ω/t
I=mr^2
τ = Iα =mr^2 ω/t = mω r^2 /t

so, τ = mω r1^2 /t1 = mω r2^2 /t2
or, r1^2 /t1 = r2^2 /t2
or, t2= r2^2 / r1^2 * t1 = 0.46^2 / 0.046^2 * 7.4 = 434.96