15. A disc is free to rotate about an axis passing through its centre and perpendicular to its plane. The moment of inertia o the disc about its rotation axis is I. A light ribbon is tightly wrapped over it in multiple layers. The end of the ribbon is pulled out at a constant speed of u. Let the radius of the ribboned disc be R at any time and thickness of the ribbon be d (<< R). Then the force (F) required to pull the ribbon as a function of radius R is:


$$\begin{gathered} \left(1\right) \frac{Id{u}^2}{2{\mathrm{\pi R}}^4} \\ \left(2\right) \frac{Id{u}^2}{3{\mathrm{\pi R}}^4} \\ \left(3\right) \frac{2Id{u}^2}{{\mathrm{\pi R}}^4} \\ \left(4\right) \frac{3Id{u}^2}{{\mathrm{\pi R}}^4} \end{gathered}$$