Physical World Units and Measurements - Result Question 30
32. According to Newton, the viscous force acting between liquid layers of area $A$ and velocity gradient $\Delta V / \Delta Z$ is given by $F=-\eta A \frac{\Delta V}{\Delta Z}$ where $\eta$ is constant called coefficient of viscosity. The dimensional formula of $\eta$ is
(a) $ML^{-2} T^{-2}$
(c) $ML^{2} T^{-2}$
(b) $M^{0} L^{0} T^{0}$
(d) $ML^{-1} T^{-1}$
[1990]
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Answer:
Correct Answer: 32. (d)
Solution:
(d) $F=-\eta A \frac{\Delta V}{\Delta Z}$
$\Rightarrow \eta=(-1) \frac{F \Delta Z}{A \Delta V}$
So dimensional formula of $\eta$
$\Rightarrow \frac{[MLT^{-2}][L]}{[L^{2}][LT^{-1}]}$
$\Rightarrow[ML^{-1} T^{-1}]$
