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Difficulty: EasyDimensions of Physical Quantities and Dimensional Analysis

Which of the following expressions represents the correct dimensions of pressure?

  1. ML−1T−2M L^{-1} T^{-2}Answer
  2. B
    MLT−2M L T^{-2}
  3. C
    ML2T−2M L^2 T^{-2}
  4. D
    ML−2T−2M L^{-2} T^{-2}

Answer

ML−1T−2M L^{-1} T^{-2}
Pressure is defined as Force divided by Area. Substituting the fundamental dimensions gives Force as MLT−2M L T^{-2} and Area as L2L^2. Dividing Force by Area results in MLT−2L2=ML−1T−2\frac{M L T^{-2}}{L^2} = M L^{-1} T^{-2}. Therefore, the expression ML−1T−2M L^{-1} T^{-2} is correct.

Step-by-Step Solution

1
State the physical definition formula for pressure
Pressure P=ForceAreaP = \frac{\text{Force}}{\text{Area}}
Pressure is defined as force applied perpendicular to a surface per unit area.
2
Substitute fundamental dimensions for force and area
[P]=[MLT−2][L2][P] = \frac{[M L T^{-2}]}{[L^2]}
Force has dimensions MLT−2M L T^{-2} and area has dimensions L2L^2.
3
Simplify the index of length LL
[P]=ML1−2T−2=ML−1T−2[P] = M L^{1 - 2} T^{-2} = M L^{-1} T^{-2}
Applying the rules of indices for length gives L1⋅L−2=L−1L^1 \cdot L^{-2} = L^{-1}.

Key Concept

Dimensions of Pressure
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Topics

Dimensions of Physical Quantities and Dimensional Analysis

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