First slide

Dimensions of physical quantities

Question

A student forgot Newton's formula for speed of sound but he remembers that there were speed (v), pressure (p) and density (d) in the formula. He then starts using dimensional analysis to find the actual relation by assuming $v \propto p^{x} d^{y}$ . The value of $x - y$ is:

Moderate

Solution

$\begin{array}{l} v \propto p^{x} d^{y} \Rightarrow [v] = [p^{x} d^{y}] \\ \Rightarrow [L T^{- 1}] = [{(M L^{- 1} T^{- 2})}^{x} {(M L^{- 3})}^{y}] \\ By comparing powers of M, L and T \\ x + y = 0, - x - 3 y = 1, - 2 x = - 1 \\ \Rightarrow x = \frac{1}{2}, y = - \frac{1}{2} \\ \Rightarrow x - y = \frac{1}{2} - (- \frac{1}{2}) = 1 \end{array}$

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