A plastic circular disc of radius $R$ is placed on a thin oil film, spread over a flat horizontal surface. The torque required to spin the disc about its central vertical axis with a constant angular velocity is proportional to
Diffcult
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Let coefficient of viscosity $\&$ thickness of film
$\rightarrow \eta \&$ x respectively
Viscous force on element ring is
$\mathrm{dF}=\eta(2 \pi \mathrm{rdr})\left[\frac{\mathrm{wr}-0}{\mathrm{x}}\right]$
$\mathrm{d} \tau=(\mathrm{dF}) r$
$\therefore \tau=\frac{\eta 2 \pi \mathrm{w}}{\mathrm{t}} \int_{0}^{\mathrm{R}} \mathrm{r}^{3} \cdot \mathrm{dr}=\left(\frac{\eta(2 \pi) \mathrm{w}}{4 \mathrm{x}}\right) \mathrm{R}^{4}$
$\therefore \tau \propto R^{4}$
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