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Question

(D) Pressure head is defined as $h = \frac{P}{ho g}$.$1$. Dimensional formula of Pressure $(P)$: $\frac{	ext{Force}}{	ext{Area}} = \frac{[MLT^{-2}

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$[M^0 L^1 T^0]$

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(D) Pressure head is defined as $h = \frac{P}{ho g}$.$1$. Dimensional formula of Pressure $(P)$: $\frac{	ext{Force}}{	ext{Area}} = \frac{[MLT^{-2}]}{[L^2]} = [ML^{-1}T^{-2}]$.$2$. Dimensional formula of Density $(ho)$: $\frac{	ext{Mass}}{	ext{Volume}} = \frac{[M]}{[L^3]} = [ML^{-3}]$.$3$. Dimensional formula of acceleration due to gravity $(g)$: $[LT^{-2}]$.Substituting these into the formula:$	ext{Pressure head} = \frac{[ML^{-1}T^{-2}]}{[ML^{-3}] 	imes [LT^{-2}]}$$= \frac{[ML^{-1}T^{-2}]}{[ML^{-2}T^{-2}]}$$= [M^{1-1} L^{-1-(-2)} T^{-2-(-2)}]$$= [M^0 L^1 T^0]$.

Column-$1$	Column-$2$
$(a)$ Wave vector	$(i)$ $M^1L^0T^{-3}$
$(b)$ Linear mass density	$(ii)$ $M^1L^{-1}T^{-2}$
$(c)$ Intensity of a wave	$(iii)$ $M^0L^{-1}T^0$
$(d)$ Volume elasticity coefficient	$(iv)$ $M^1L^{-1}T^0$

The dimensional formula for pressure head is ............

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Match Column-$1$ with Column-$2$.
Column-$1$ Column-$2$
$(a)$ Wave vector $(i)$ $M^1L^0T^{-3}$
$(b)$ Linear mass density $(ii)$ $M^1L^{-1}T^{-2}$
$(c)$ Intensity of a wave $(iii)$ $M^0L^{-1}T^0$
$(d)$ Volume elasticity coefficient $(iv)$ $M^1L^{-1}T^0$

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