Consider a 20   kg uniform circular disk of radius 0 . 2   m . It is pin supported at its center…

Consider a $20 \mathrm{kg}$ uniform circular disk of radius $0.2 \mathrm{m}$. It is pin supported at its center and is at rest initially. The disk is acted upon by a constant force $F=20 \mathrm{N}$ through a massless string wrapped around its periphery as shown in the figure.

Suppose the disk makes $n$ number of revolutions to attain an angular speed of $50 \mathrm{rad} {\mathrm{s}}^{-1}$. The value of $n$, to the nearest integer, is _______ .

[Given : In one complete revolution, the disk rotates by $6.28 \mathrm{rad}$]