First slide

Dimensions

Question

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

Easy

A

$[M^{2} L T^{- 3}]$
B

$[M L T^{- 2}]$
C

$[L T^{- 3}]$
D

$[M L^{3} T^{- 1}]$

Solution

$P = \frac{a - t^{2}}{b x^{2}} = \frac{a}{b x^{2}} - \frac{t^{2}}{b x^{2}}$
As per principle of dimensional homogeneity each term in the equation must carry the dimension of pressure.
$\begin{array}{l} [P] = [\frac{a}{b x^{2}}] \Rightarrow [\frac{a}{b}] = [P] [x^{2}] = [M L^{- 1} T^{- 2}] [L^{2}] \\ \Rightarrow [\frac{a}{b}] = [M L T^{- 2}] \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App