Physics

# In the relation $V=\dfrac { \pi }{ 8 } \dfrac { { Pr }^{ 4 } }{ tl }$, $P$ is pressure, $r$ is the radius, $t$ is time and $l$ is length. The dimensions of $V$ are:

${ M }^{ 1 }{ L }^{ 2 }{ T }^{-3}$

##### SOLUTION
$\pi$ is dimensionless, thus $|V| = \dfrac{|P||r^4|}{|t||l|}$
Now, $Pressure = \dfrac{Force}{Area}$, thus its dimensions are $\dfrac{MLT^{-2}}{L^2}=ML^{-1}T^{-2}$
Thus, $|V|=\dfrac{ML^{-1}T^{-2}L^4}{TL} = ML^2T^{-3}$

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Single Correct Medium Published on 18th 08, 2020
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