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Q.

The critical angular velocity w of a cylinder inside another cylinder containing a liquid at which its turbulence occurs depends on viscosity η , density d and the distance x between the walls of the cylinders. Then w is proportional to

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a

η2xd

b

ηd2x

c

ηx2d

d

xdη

answer is A.

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Detailed Solution

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ωαηadbXcT−1∝ML−1T−1aML−3bLcT−1∝Ma+bL−a−3b+cT−a−a=−1⇒a=1a+b=0⇒b=−1−a−3b+c=0⇒c=−2ω∝ηdx2

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