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Q.

A highly viscous liquid of viscosity coefficient  η   flows through a fixed horizontal cylindrical tube (fixed from outer surface) of internal radius r, thickness  t(t<<r)   and length l. Volume of liquid flowing per second is Q and pressure difference across the tube is P. Modulus of rigidity of material of tube is β . Shear strain in the tube will be: (Take,Q=πpr48ηl)  

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a

πβr316ηQ

b

4ηQπβr3

c

8ηQπβr2

d

βr38ηQ

answer is B.

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Detailed Solution

Q=πpR48ηlPηl=8QπR4 V=P4ηl{R2r2}|dVdr|=Pr2ηl=4QrπR4   Spear stress on liquid at r=R τ=η|dvdr|=4QηπR3 Spear stress on solid  =4QηπR3 Spear stress of solid  =4QηπβR3

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