Question

Which of the following ratios express pressure?

1. Force/Area
2. Energy/Volume
3. Energy/Area
4. Force/ Volume

Answer 1

a. Force/Area

b. Energy/Volume

Explanation:

We can express the ratio as pressure (P) if the dimension of the ratio is the same as that of pressure. 

So, we will check the dimension of each option whether it is equal to P or not.

a. Dimension of ${\displaystyle \frac{F}{A}=\frac{\left[ML{T}^{-2}\right]}{\left[L^2\right]}}$

⇒ ${\displaystyle \left[M{L}^{-1}{T}^{-2}\right]}$ = dimension of P

b. Dimension of ${\displaystyle \frac{E}{V}=\frac{\left[M{L}^2{T}^{-2}\right]}{\left[L^3\right]}}$

⇒ ${\displaystyle \left[M{L}^{-1}{T}^{-2}\right]}$ = dimension of P

c. Dimension of ${\displaystyle \frac{E}{A}=\frac{\left[M{L}^2{T}^{-2}\right]}{\left[L^2\right]}}$

⇒ ${\displaystyle \left[M{L}^0{T}^{-2}\right]}$ ≠ dimension of P

d. Dimension of ${\displaystyle \frac{F}{V}=\frac{\left[ML{T}^{-2}\right]}{\left[L^3\right]}}$

⇒ ${\displaystyle \left[M{L}^{-2}{T}^{-2}\right]}$ ≠ dimension of P