Understanding Pressure Dimensions
Pressure is defined as the force exerted per unit area. The dimensional formula of pressure can be derived as follows:
- Pressure (P) = Force (F) / Area (A)
Given that:
- Force has the dimension of [M L T^-2]
- Area has the dimension of [L^2]
Thus, the dimension of pressure can be calculated as:
- P = [M L T^-2] / [L^2] = [M L^-1 T^-2]
This indicates that pressure has dimensions of mass per unit length per unit time squared.
Comparative Analysis of Options
Now, let's analyze the options provided:
- a) Energy per unit volume
- Energy (E) has the dimension of [M L^2 T^-2].
- Volume (V) has the dimension of [L^3].
- Therefore, Energy per unit volume = [M L^2 T^-2] / [L^3] = [M L^-1 T^-2].
- This matches the dimension of pressure.
- b) Energy
- Energy has the dimension of [M L^2 T^-2], which does not match pressure dimensions.
- c) Force per unit volume
- Force (F) has the dimension of [M L T^-2].
- Therefore, Force per unit volume = [M L T^-2] / [L^3] = [M L^-2 T^-2], which differs from pressure dimensions.
- d) Force
- Force has the dimension of [M L T^-2], which is also not the same as pressure.
Conclusion
The only option that shares the same dimensional formula as pressure is:
- a) Energy per unit volume