First slide

Dimensions of physical quantities

Question

Is the given expression of velocity of sound given by $v = \sqrt{(\frac{E}{ρ})}$ is dimensionally correct?
Here, E = coefficient of elasticity,
$ρ =$ density of medium

Moderate

A

Yes
B

No
C

Cannot be predicted
D

The correct expression is $\frac{E}{ρ}$

Solution

$[L H S] = [v] = [L T^{- 1}]$
$[R H S] = [{(\frac{E}{ρ})}^{1 / 2}]$
$= [{(\frac{M L^{- 1} T^{- 2}}{M L^{- 3}})}^{1 / 2}] = [L T^{- 1}]$
[LHS] = [RHS]
Hence, equation is dimensionally correct.

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