A) \[M{{L}^{-1}}{{T}^{-2}}\]
B) \[{{M}^{0}}L{{T}^{-2}}\]
C) \[ML{{T}^{-2}}\]
D) \[M{{L}^{2}}{{T}^{-2}}\]
Correct Answer: A
Solution :
Young?s modulus \[=\frac{\text{Strees}}{\text{Strain}}\] \[Stress\,=\frac{Force}{Area}\Rightarrow [\sigma ]=\frac{\left[ ML{{T}^{-2}} \right]}{[{{L}^{2}}]}=[M{{L}^{-1}}{{T}^{-2}}]\] \[\text{Strain=}\frac{\text{Change}\,\text{in}\,\text{length}}{\text{Original}\,\text{length}}\] Hence strain is dimensionless Hence, \[[Y]=[M{{L}^{-1}}{{T}^{-2}}]\]
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