# The dimensions of shear stress is the same as ______.

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The dimensions of shear stress is the same as ______.
1. Volume
2. Pressure
3. Force
4. Dimensionless

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Correct Answer - Option 2 : Pressure

CONCEPT:

• Shear stress: Force F|| applied along the object's parallel surface divided by the cross-section area A of the surface on which the parallel force is acting.
$\rm Shear~Stress = {F_{||} \over A}$
• The dimension of shear stress is:
$\rm [Shear~stress] = {[F]\over [A]}={[MLT^{-2}]\over [L^2]}=[ML^{-1}T^{-2}]$

EXPLANATION:

• Option 1: Dimension of volume is [L3].
• Option 2: Dimension of Pressure (Force per unit area) is
$\rm Pressure = {F \over A}$
$\rm [Pressure] = {[F]\over [A]}={[MLT^{-2}]\over [L^2]}=[ML^{-1}T^{-2}]$

The dimensions of pressure are the same as the dimension of shear stress.

• Option 3: Dimension of force is [MLT-2]
• So the correct answer is option 2.

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