JEE Main · 2004 · 24 Apr 2004 · Offline · Fluid Mechanics

Which one of the following represents the correct dimensions of the coefficient of viscosity?

(A) $ML^{- 1} T^{- 2}$
(B) $MLT^{- 1}$
(C) $M L^{- 1} T^{- 1}$ ✓ Correct
(D) $ML^{- 2} T^{- 2}$

Answer: (C)

Solution

The coefficient of viscosity is defined through the viscous force as the force acting per unit area per unit velocity gradient. Writing each piece dimensionally, force is

M L T^{- 2}

, area is

L^{2}

, and the velocity gradient is a velocity divided by a length, which is

T^{- 1}

. Dividing through,

η = \frac{M L T ^{- 2}}{L ^{2} \cdot T ^{- 1}} = M L^{- 1} T^{- 1}

, so the coefficient of viscosity carries the dimensions

M L^{- 1} T^{- 1}

JEE Main · 2004 · 24 Apr 2004 · Offline · Single correct option

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