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Q.

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 :

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a

$R^{2}$

b

$R^{3}$

c

$R^{4}$

d

$R^{6}$

answer is C.

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Detailed Solution

Let coefficient of viscosity and thickness of film $\to η$ and x respectively
Question Image
Viscous force on element ring is
$d F = η (2 π r d r) [\frac{w r - 0}{x}] d τ = (d F) r ∴ τ = \frac{η 2 π w}{t} \int_{0}^{R} r^{3} . d r = (\frac{η (2 π) w}{4 x}) R^{4} ∴ τ \infty R^{4}$

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