Question

Consider a $20kg$ uniform circular disk of radius $0.2m$. It is pin supported at its center and is at rest initially. The disk is acted upon by a constant force $F=20N$ 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 $50rad{s}^{-1}$. The value of $n$, to the nearest integer, is_____ [Given : In one complete revolution, the disk rotates by $6.28rad]$

Answer 1

Answer: 20

$\alpha =\frac{\tau }{I}=\frac{F\cdot R.}{m{R}^2/2}=\frac{2F}{mR}$
$\alpha =\frac{2\times 200}{20\times (0.2)}=10rad/s^2$
${\omega }^2={\omega }_0^2+2\alpha \Delta \theta$
$(50{)}^2=0^2+2(10)\Delta \theta \Rightarrow \Delta \theta =\frac{2500}{20}$
$\Delta \theta =125rad$
No. of revolution $=\frac{125}{2\pi }\approx 20$ revolution