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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

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Cannot be predicted

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

Yes

answer is A.

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Detailed 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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