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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

R4

b

R3

c

R2

d

R6

answer is C.

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Detailed Solution

Let coefficient of viscosity and thickness of filmη   and x respectively
 Question Image
Viscous force on element ring is 
 dF=η(2πrdr)[wr0x] dτ=(dF)r    τ=η2πwt0Rr3.dr=(η(2π)w4x)R4 τR4
 
 
 
 

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