The dimensional formula for volume elasticity | vedclass

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Question

(D) Volume elasticity (Bulk Modulus) is defined as the ratio of stress to volumetric strain.Volume elasticity = $\frac{	ext{Stress}}{	ext{Volumetric

Vedclass · Accepted Answer

$M^1 L^{-1} T^{-2}$

Vedclass · Answer

(D) Volume elasticity (Bulk Modulus) is defined as the ratio of stress to volumetric strain.Volume elasticity = $\frac{	ext{Stress}}{	ext{Volumetric strain}} = \frac{	ext{Force/Area}}{	ext{Change in volume/Original volume}}$.Since strain is a ratio of two similar quantities (change in volume/original volume),it is dimensionless.Therefore,the dimensions of volume elasticity are the same as the dimensions of stress (Force/Area).Dimensional formula of Force = $[M^1 L^1 T^{-2}]$.Dimensional formula of Area = $[L^2]$.Dimensional formula of Volume elasticity = $\frac{[M^1 L^1 T^{-2}]}{[L^2]} = [M^1 L^{-1} T^{-2}]$.Thus,the correct option is $D$.

The dimensional formula for volume elasticity is:

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