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Question

When a solid sphere moves through a liquid, the liquid opposes the motion with a force F. The 

magnitude of F depends on the coefficient of viscosity η of the liquid, the radius r of the sphere and the speed v of the sphere.

Assuming that F is proportional to different powers of these quantities, guess a formula for F using the 

method of dimensions. Use F = -ηA(v2v1)x2x1



Correct Answer
A

Your Answer
B

Your Answer
C

Your Answer
D

None of these


Solution

The correct option is A


Suppose the formula is F=kηarbvc

η=[ML1T1]

Then, MLT2=[ML1T1]aLb(LT)c

= MaLa+b+cTac

Equating the exponents of M, L and T from both sides,

a = 1

-a + b + c = 1

-a - c = -2

Solving these, a = 1, b = 1, and c = 1

Thus, the formula for F is F=kηrv

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