Physical World Units and Measurements - Result Question 27
29. Turpentine oil is flowing through a tube of length $\ell$ and radius $r$. The pressure difference between the two ends of the tube is $p$. The viscosity of oil is given by
$ \eta=\frac{p(r^{2}-x^{2})}{4 v l} $
where $v$ is the velocity of oil at a distance $x$ from the axis of the tube. The dimensions of $\eta$ are
(a) $[M^{0} L^{0} T^{0}]$
(c) $[ML^{2} T^{-2}]$
(b) $[MLT^{-1}]$
(d) $[ML^{-1} T^{-1}]$
[1993]
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Answer:
Correct Answer: 29. (d)
Solution:
- (d)
$ \begin{aligned} \eta & =\frac{p(r^{2}-x^{2})}{4 v l}=\frac{[ML^{-1} T^{-2}][L^{2}]}{[LT^{-1}][L]} \\ & =[ML^{-1} T^{-1}] \end{aligned} $
According to the principle of homogeneity, the dimensions of each term on the L.H.S. must be equal to the dimensions of the terms on the R.H.S. Only then dimensional equation or formula is dimensionally correct.
