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Dimensional Analysis

Question

The dimensions of energy per unit volumes are the same as those of :
Work
Stress
Modulus
Pressure

A

Stress

B

Modulus

C

Work

D

Pressure

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Solution

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The dimension of energy per unit volume is equal to the dimension of pressure.

Firstly, the dimension of energy is : $[M L^{2} T^{- 2}]$

The dimension of volume: $[L^{3}]$

The dimension of pressure : $[L^{- 1} M T^{- 2}]$

Now, $\frac{e n e r g y}{v o l u m e} = \frac{[M L^{2} T^{- 2}]}{[L^{3}]} = [L^{- 1} M T^{- 2}]$

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