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Question

Stoke's law states that the viscous drag force F experience by a sphere of radius a, moving with a speed v through a fluid with coefficient of viscosity η, is given by F =6πηav If this fluid is flowing through a cylindrical pipe of radius r, length l and a pressure difference of P across its two ends, then the volume of water V which flows through the pipe in time t can be written as

Vt=k(Pl)aηbrc

Where k is a dimensionless constant. Correct values of a, b and c are


A

a = 1, b = – 1, c = 4

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B

a = – 1, b = 1, c = 4

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C

a = 2, b = – 1, c = 3

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D

a = 1, b = – 2, c = – 4

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Solution

The correct option is A

a = 1, b = – 1, c = 4


Vt=k(Pl)aηbrc
L3T1=(ML2T2)aLc(ML1T1)b
a + b = 0
-2a - b + c = 3
-2a - b = -1
c = 4, a = 1, b = -1
Answer (A) is correct.


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