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CGP EDU Academic Team
Published on: September 12, 2026
The dimensional formula for young's modulus is
Text Solution
Verified by ExpertsThe correct answer is:
C
Young's modulus (E) is defined as the ratio of stress to strain.
Stress is defined as force per unit area, which has the dimensional formula:
\[ \text{Stress} = \frac{Force}{Area} = \frac{[M][L][T^{-2}]}{[L^2]} = [M][L^{-1}][T^{-2}] \]
On the other hand, strain is a dimensionless quantity (change in length/original length), hence has no dimensions.
Therefore, the dimensional formula for Young's modulus is:
\[ E = \frac{Stress}{Strain} = [M][L^{-1}][T^{-2}] \]
So the correct answer is option C: [M][L^{-1}][T^{-2}].
Stress is defined as force per unit area, which has the dimensional formula:
\[ \text{Stress} = \frac{Force}{Area} = \frac{[M][L][T^{-2}]}{[L^2]} = [M][L^{-1}][T^{-2}] \]
On the other hand, strain is a dimensionless quantity (change in length/original length), hence has no dimensions.
Therefore, the dimensional formula for Young's modulus is:
\[ E = \frac{Stress}{Strain} = [M][L^{-1}][T^{-2}] \]
So the correct answer is option C: [M][L^{-1}][T^{-2}].
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