Question

Can you please answer by question dear friends.......

Answer 1

The axis of rotation is considered to pass through the center of the meter scale through the center of the scale, so that the two discs, each are 0.5 m apart from the axis of rotation. Also, assume the meter scale is massless.

We note that the axis of rotation is parallel to an axis passing through the diameter of the disc.

So the moment of inertia of a disc about an axis passing through one of its diameter, we know that, is MR²/4.

Hence, by theorem of parallel axes, the moment of inertia of the disc about the actual axis is,

I1 = MR²/4 + M(0.5)²

I1 = M(R² + 1)/4

In case of the other disc, is the same, i.e.,

I2 = M(R² + 1)/4

Then, the total moment of inertia of the system,

I = I1 + I2

I = M(R² + 1)/2