Dimensional formula for pressure head is

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Question

(D) Pressure head is defined as $h = \frac{P}{\rho g}$,where $P$ is pressure,$\rho$ is density,and $g$ is acceleration due to gravity.Dimensional form

Vedclass · Accepted Answer

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

Vedclass · Answer

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

Column-$I$	Column-$II$
$(A)$ Electrical resistance	$(p)$ $M L^3 T^{-3} A^{-2}$
$(B)$ Electrical potential	$(q)$ $M L^2 T^{-3} A^{-2}$
$(C)$ Specific resistance	$(r)$ $M L^2 T^{-3} A^{-1}$
$(D)$ Specific conductance	$(s)$ None of these

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Match the following two columns:

Column-$I$ Column-$II$

$(A)$ Electrical resistance $(p)$ $M L^3 T^{-3} A^{-2}$

$(B)$ Electrical potential $(q)$ $M L^2 T^{-3} A^{-2}$

$(C)$ Specific resistance $(r)$ $M L^2 T^{-3} A^{-1}$

$(D)$ Specific conductance $(s)$ None of these

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