Pressure has the same dimension as
Correct Answer :
energy per unit volume
Solution :
The correct option is "energy per unit volume".
To understand why this option is correct, let us find and compare the dimensional formulas for pressure and energy per unit volume step-by-step.
Step 1: Find the dimensions of Pressure
Pressure is defined as force per unit area:
Pressure = Force / Area
The dimensional formula of Force is given by mass times acceleration:
[Force] = [M] [L T-2] = [M L T-2]
The dimensional formula of Area is:
[Area] = [L2]
Therefore, the dimensional formula of Pressure is:
[Pressure] = [M L T-2] / [L2]
Step 2: Find the dimensions of Energy per unit volume
Energy per unit volume is defined as:
Energy per unit volume = Energy / Volume
The dimensional formula of Energy (which is equivalent to Work = Force × Distance) is:
[Energy] = [Force] × [Distance] = [M L T-2] × [L] = [M L2 T-2]
The dimensional formula of Volume is:
[Volume] = [L3]
Therefore, the dimensional formula of Energy per unit volume is:
[Energy per unit volume] = [M L2 T-2] / [L3]
Conclusion
Comparing the results from Step 1 and Step 2, we can see that both pressure and energy per unit volume have the exact same dimensional formula, which is [M L-1 T-2]. Thus, pressure has the same dimension as energy per unit volume.
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