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Question

Physics Question on Viscosity

The coefficient of viscosity has following dimensions

A

M−1L2T3M^{-1}L^2T^3

B

ML−1T−2ML^{-1}T^{-2}

C

ML−2T−1ML^{-2}T^{-1}

D

ML−1T−1ML^{-1}T^{-1}

Answer

ML−1T−1ML^{-1}T^{-1}

Explanation

Solution

Using F=6 π η r vF =6 \,\pi\, \eta\, r\, v we get
[η]=[F][r][v]=[MLT−2][L][LT−1][\eta]=\frac{[F]}{[r][v]}=\frac{\left[M L T^{-2}\right]}{[L]\left[L T^{-1}\right]}
=ML−1 T−1=M L^{-1} \,T^{-1}