Pressure P=(a t^2 / b x) where x= distance, t= time find the dimensional formula for a / b (a) M

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Pressure P=(a t^2 / b x) where x= distance, t= time find the...

Pressure $P=\left(a t^{2} / b x\right)$ where $x=$ distance, $t=$ time find the dimensional formula for $\mathrm{a} / \mathrm{b}$ (a) $\mathrm{M}^{1} \mathrm{~L}^{0} \mathrm{~T}^{-4}$ (b) $\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-1}$ (c) $\mathrm{M}^{1} \mathrm{~L}^{0} \mathrm{~T}^{-2}$ (d) $\mathrm{M}^{+1} \mathrm{~L}^{0} \mathrm{~T}^{-2}$

Pressure $P=\left(a t^{2} / b x\right)$ where $x=$ distance, $t=$ time find the dimensional formula for $\mathrm{a} / \mathrm{b}$
(a) $\mathrm{M}^{1} \mathrm{~L}^{0} \mathrm{~T}^{-4}$
(b) $\mathrm{M}^{1} \mathrm{~L}^{1} \mathrm{~T}^{-1}$
(c) $\mathrm{M}^{1} \mathrm{~L}^{0} \mathrm{~T}^{-2}$
(d) $\mathrm{M}^{+1} \mathrm{~L}^{0} \mathrm{~T}^{-2}$

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Key Concepts

Dimensional Analysis

Dimensional analysis is a technique used to express physical quantities in terms of their fundamental dimensions (such as mass, length, and time) and to check the consistency of equations. It is essential for deducing the dimensions of constants and ensuring that both sides of an equation are dimensionally equivalent.

Pressure

Pressure is defined as force per unit area and has a standard dimensional formula derived from the dimensions of force (mass times acceleration). Its proper understanding is key when relating pressure to other physical quantities in equations.

Dimensional Consistency

Dimensional consistency refers to the requirement that all terms in a physical equation must have the same dimensions. This concept is fundamental for verifying the validity of equations and for deriving the dimensions of unknown constants.

Algebraic Manipulation in Dimensional Analysis

Algebraic manipulation involves rearranging the dimensional equations to isolate and solve for the unknown constants or ratios. This method is instrumental in deriving the dimensional formulas of composite parameters by equating dimensions on both sides of the equation.

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