Question

The dimensions of pressure are same as that of

• A. Energy
• B. Energy per unit volume
• C. Force
• D. Force per unit volume.

Answer 1

The Correct Option is B

 The question asks us to determine which option has the same dimensions as pressure. We need to understand the dimensional formula of pressure and compare it with the other given options.

Dimensions of Pressure:
Pressure is defined as force per unit area. The formula for pressure (\(P\)) is given by:

\(P = \frac{F}{A}\)

Where:

• \(F\) is the force with dimensions \([M^1L^1T^{-2}]\) (mass \(\times\) acceleration), and
• \(A\) is the area with dimensions \([L^2]\).

Thus, the dimensional formula of pressure is:

\(P = \frac{[M^1L^1T^{-2}]}{[L^2]} = [M^1L^{-1}T^{-2}]\)

Dimensions of Options:

1. Energy: Energy has dimensions of \([M^1L^2T^{-2}]\).
2. Energy per unit volume: This is energy divided by volume. Since volume has dimensions of \([L^3]\), energy per unit volume has dimensions of:

 

\([M^1L^2T^{-2}] \div [L^3] = [M^1L^{-1}T^{-2}]\)

1. Force: Force has dimensions of \([M^1L^1T^{-2}]\).
2. Force per unit volume: Force per unit volume has dimensions of:

 

\([M^1L^1T^{-2}] \div [L^3] = [M^1L^{-2}T^{-2}]\)

After comparing these dimensions, we can see that "energy per unit volume" has the same dimensions as pressure, i.e., \([M^1L^{-1}T^{-2}]\).

Conclusion: The correct answer is option (b) Energy per unit volume.

Tip: Always remember that pressure is force over an area, and its dimensions are critical in many physics calculations, especially when comparing with other physical quantities.