Dimensional formula of a b satisfying P = a - t 2 bx where P is pressure, x is distance and t is time will be

P = a - t 2 b x = a b x - t 2 b x By the principle of homogeneity. [ P ] = force area = a b [ x ] M L - 1 T - 2 = a b 1 L ⇒ a b = M T - 2

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Physics - Unit & Dimension Question with Solution | TestHub

PhysicsUnit & DimensionMiscellaneousEasy2 minPYQ_2020

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Dimensional formula of $\frac{a}{b}$ satisfying $P = \frac{a - t^{2}}{bx}$ where $P$ is pressure, $x$ is distance and $t$ is time will be

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Solution:

$P = \frac{a - t^{2}}{b x} = \frac{a}{b x} - \frac{t^{2}}{b x}$
By the principle of homogeneity.
$[P] = \frac{force}{area} = \frac{a}{b [x]}$
$M L^{- 1} T^{- 2} = \frac{a}{b} [\frac{1}{L}] \Rightarrow \frac{a}{b} = M T^{- 2}$

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:Unit & DimensionSubtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2020

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