(C) The given formula is $X = \frac{\pi}{3}(a^2 - b^2) h d$. Since $a, b,$ and $h$ are lengths,their dimensional formula is $[L]$. Thus,$(a^2 - b^2)$

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(C) The given formula is $X = \frac{\pi}{3}(a^2 - b^2) h d$. Since $a, b,$ and $h$ are lengths,their dimensional formula is $[L]$. Thus,$(a^2 - b^2)$ has dimensions $[L^2]$. The term $h$ has dimensions $[L]$. The term $d$ is density,which is defined as $\frac{\text{mass}}{\text{volume}}$,so its dimensions are $[M L^{-3}]$. Substituting these dimensions into the formula: $[X] = [L^2] \cdot [L] \cdot [M L^{-3}] = [L^3] \cdot [M L^{-3}] = [M]$. Since the resulting dimension is $[M]$,the physical quantity is mass.

Class 11 Physics Units, Dimensions and Measurement Dimensional Analysis, Uses and Limitations

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$A$ certain physical quantity is calculated from the formula $\frac{\pi}{3}(a^2-b^2) h d$,where $a, b$ and $h$ are all lengths and $d$ is density. The physical quantity being calculated is

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Dimensional Analysis, Uses and Limitations

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$A$ certain physical quantity is calculated from the formula $\frac{\pi}{3}(a^2-b^2) h d$,where $a, b$ and $h$ are all lengths and $d$ is density. The physical quantity being calculated is

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