Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

Test If the Following Equations Are Dimensionally Correct: V = √ P ρ , - Physics

Sum

Test if the following equation is dimensionally correct:
$v = \sqrt{\frac{P}{\rho}},$

where v = frequency, ρ = density, P = pressure,

Solution

$\nu = \sqrt{\left( \frac{P}{\rho} \right)}$
Velcocity, [ν] = [LT−1]
Pressure,
$P = \frac{\left[ F \right]}{\left[ A \right]} = \left[ {ML}^{- 1} T^{- 2} \right]$
Density,
$\left[ \rho \right] = \frac{\left[ M \right]}{\left[ V \right]} = \left[ {ML}^{- 3} T^0 \right]$
Now,
$\sqrt{\frac{P}{\rho}} = \left[ \frac{\left[ {ML}^{- 1} T^{- 2} \right]}{\left[ {ML}^{- 3} \right]} \right]^\frac{1}{2} = \left[ L^2 T^{- 2} \right]^{1/2} = \left[ {LT}^{- 1} \right]$

Since the dimensions of both sides of the equation are the same, the equation is dimensionally correct.

Concept: What is Physics?
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APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 1
Chapter 1 Introduction to Physics
Exercise | Q 18.2 | Page 10
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