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1.Units, Dimensions and Measurement
medium
Pressure gradient has the same dimension as that of
AVelocity gradient
BPotential gradient
CEnergy gradient
DNone of these
Solution
(d) Velocity gradient $ = \frac{v}{x} = \frac{{[L{T^{ – 1}}]}}{{[L]}} = [{T^{ – 1}}]$
Potential gradient$ = \frac{V}{x} = \frac{{[M{L^2}{T^{ – 3}}{A^{ – 1}}]}}{{[L]}}$$ = [ML{T^{ – 3}}{A^{ – 1}}]$
Energy gradient $ = \frac{E}{x} = \frac{{[M{L^2}{T^2}]}}{{[L]}} = [ML{T^{ – 2}}]$
and pressure gradient$ = \frac{P}{x} = \frac{{[M{L^{ – 1}}{T^{ – 2}}]}}{{[L]}} = [M{L^{ – 2}}{T^{ – 2}}]$
Potential gradient$ = \frac{V}{x} = \frac{{[M{L^2}{T^{ – 3}}{A^{ – 1}}]}}{{[L]}}$$ = [ML{T^{ – 3}}{A^{ – 1}}]$
Energy gradient $ = \frac{E}{x} = \frac{{[M{L^2}{T^2}]}}{{[L]}} = [ML{T^{ – 2}}]$
and pressure gradient$ = \frac{P}{x} = \frac{{[M{L^{ – 1}}{T^{ – 2}}]}}{{[L]}} = [M{L^{ – 2}}{T^{ – 2}}]$
Standard 11
Physics
