Question:
Which pair of physical quantities have same dimensional formula?
Which pair of physical quantities have same dimensional formula?
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Pressure, stress, and modulus of elasticity all have the same dimensional formula \(ML^{-1}T^{-2}\).
Updated On: May 7, 2026
- Torque and momentum
- Surface tension and tension
- Pressure and modulus of elasticity
- Force constant and Planck's constant
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The Correct Option is C
Solution and Explanation
We need to identify the pair having the same dimensional formula.
Pressure is defined as:
\[
\text{Pressure}=\frac{\text{Force}}{\text{Area}}.
\]
The dimensional formula of force is:
\[
[F]=MLT^{-2}.
\]
The dimensional formula of area is:
\[
[A]=L^2.
\]
Therefore,
\[
[\text{Pressure}]=\frac{MLT^{-2}}{L^2}.
\]
\[
[\text{Pressure}]=ML^{-1}T^{-2}.
\]
Now, modulus of elasticity is defined as:
\[
\text{Modulus of elasticity}=\frac{\text{Stress}}{\text{Strain}}.
\]
Strain is dimensionless.
So,
\[
[\text{Modulus of elasticity}]=[\text{Stress}].
\]
Stress is:
\[
\text{Stress}=\frac{\text{Force}}{\text{Area}}.
\]
Therefore,
\[
[\text{Stress}]=ML^{-1}T^{-2}.
\]
Hence,
\[
[\text{Modulus of elasticity}]=ML^{-1}T^{-2}.
\]
Thus, pressure and modulus of elasticity have the same dimensional formula.
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