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# The Dimensional Formula for Youngs Modulus Is

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## Step 1: Definition and formula of Young's modulusYoung's modulus is the property of the material that tells how easily we can stretch that material.Formula: $Y=\frac{Stress}{Strain}=\frac{FL}{lA}$ Where $F$ is the force applied $L$is the original length $A$ is the area of cross-section $l$ is the deformation in the length Step 2: Finding the dimension of Young's modulusSubstitute all the dimensional formulas of $F,L,A,l$ in the formula respectively.Dimensional formula of Young's modulus, $Y=\frac{FL}{lA}\phantom{\rule{0ex}{0ex}}⇒Y=\frac{\left[{M}^{1}{L}^{1}{T}^{-2}\right]\left[{M}^{0}{L}^{1}{T}^{0}\right]}{\left[{M}^{0}{L}^{1}{T}^{0}\right]\left[{M}^{0}{L}^{2}{T}^{0}\right]}\phantom{\rule{0ex}{0ex}}⇒Y={M}^{1}{L}^{-1}{T}^{-2}$Dimensional formula of Youngs modulus $Y$ is ${M}^{1}{L}^{-1}{T}^{-2}$

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