First slide

Dimensions of physical quantities

Question

The dimension of $\frac{a}{b}$ in the equation $P = \frac{a - t^{2}}{b x}$ , where P is pressure, x is distance and t is time, is

Moderate

A

$M T^{- 2}$
B

$M^{2} L T^{- 3}$
C

$M L^{3} T^{- 1}$
D

$L T^{- 3}$

Solution

$[a] = [T^{2}] and [b] = \frac{[a - t^{2}]}{[P] [x]} = \frac{T^{2}}{[M L^{- 1} T^{- 2}] [L]}$
$\begin{array}{l} \Rightarrow [b] = [M^{- 1} T^{4}] \\ So [\frac{a}{b}] = \frac{[T^{2}]}{[M^{- 1} T^{4}]} = [M T^{- 2}] \end{array}$

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