Dimensional Analysis

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Dimensions are the powers to which the fundamental units are raised to obtain the derived unit of a physical quantity. Example: velocity has dimensions of length 1 and time -1, so its dimensional form…

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If a quantity has powers a in length, b in mass, and c in time, its dimensional formula is [L^a M^b T^c]. Here a, b, and c are the exponents of the fundamental quantities.

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Area = length × breadth. Step 1: [L] × [L] = [L^2] Step 2: Write in full form: [M^0 L^2 T^0] Answer: [M^0 L^2 T^0]…

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Density = mass / volume. Step 1: [M] / [L^3] = [M L^-3] Step 2: Write in full form: [M^1 L^-3 T^0] Answer: [M L^-3 T^0]…

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Force = mass × acceleration. Step 1: [M] × [L T^-2] = [M L T^-2] Answer: [M L T^-2]…

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Work = force × displacement. Step 1: [M L T^-2] × [L] = [M L^2 T^-2] Answer: [M L^2 T^-2]…

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Power = work / time. Step 1: [M L^2 T^-2] / [T] = [M L^2 T^-3] Answer: [M L^2 T^-3]…

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Pressure = force / area. Step 1: [M L T^-2] / [L^2] = [M L^-1 T^-2] Answer: [M L^-1 T^-2]…