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Test If the Following Equations Are Dimensionally Correct: V = 1 2 π √ M G L I ; Where H = Height, S = Surface Tension, ρ = Density, P = Pressure, V = Volume, - Physics

Sum

Test if the following equation is dimensionally correct:
\[v = \frac{1}{2 \pi}\sqrt{\frac{mgl}{I}};\] 
where h = height, S = surface tension, \[\rho\] = density, P = pressure, V = volume, \[\eta =\] coefficient of viscosity, v = frequency and I = moment of interia.

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Solution

\[\nu = \frac{1}{2\pi}\sqrt{\left( \frac{mgl}{I} \right)}\]
Frequency, ν = [T−1]

\[\sqrt{\left( \frac{mgl}{I} \right)} = \sqrt{\frac{\left[ M \right] \left[ {LT}^{- 2} \right] \left[ L \right]}{\left[ {ML}^2 \right]}}\]

\[ \Rightarrow \left[ \frac{\left[ {ML}^2 T^{- 2} \right]}{\left[ {ML}^2 \right]} \right]^\frac{1}{2} = \left[ T^{- 1} \right]\]
Since the dimensions of both sides of the equation are the same, the equation is dimensionally correct.

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APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 1 Introduction to Physics
Exercise | Q 18.4 | Page 10
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