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Question

Physics Question on Dimensional Analysis

The dimensional formula of coefficient of viscosity can be expressed as Ma LbTcM^a\, L^bT^c . What are the values of aa , bb and cc .

A

a=b=c=1a = b = c = 1

B

a=b=1a = b = 1 , c=−1c = -1

C

a=1a = 1 , b=c=−1b = c = -1

D

a=c=−1a = c = - 1 , b=1b = 1

Answer

a=1a = 1 , b=c=−1b = c = -1

Explanation

Solution

The correct answer is C:a=1,b=c=−1a=1,b=c=-1
F=6πηrvF=6\pi\eta rv
η=F6πrv\eta=\frac{F}{6\pi rv}
=MLT−2L×LT−1=\frac{MLT^{-2}}{L\times LT^{-1}}
=ML−1T−1=ML^{-1}T^{-1}