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Q.
The dimensions of $\frac{a}{b}$ in the relation $P=\frac{a-t^{2}}{bx}$ , where $P$ is the pressure, $x$ is the distance and $t$ is the time, is
KCETKCET 2003Physical World, Units and Measurements
Solution:
$\begin{array}{l}
P =\frac{ a - t ^{2}}{ bx }\\
P =\left[ ML ^{-1} T ^{-2}\right]\\
\text { a will have same unit as } t ^{2} . \text { So, } a =\left[ T ^{2}\right]\\
b =\left[\frac{ a - t ^{2}}{ px }\right]=\frac{\left[ T ^{2}\right]}{\left[ ML ^{-1} T ^{-2} L \right]}=\left[ M ^{-1} L ^{0} T ^{4}\right]\\
\frac{ a }{ b }=\frac{\left[ T ^{2}\right]}{\left[ M ^{-1} L ^{0} T ^{4}\right]}=\left[ ML ^{0} T ^{-2}\right]
\end{array}$