MCQ
Which of the following ratios express pressure?
- A$\frac{\text{Force}}{\text{Area}}.$
- B$\frac{\text{Energy}}{\text{Volume}}.$
- C$\frac{\text{Energy}}{\text{Area}}.$
- D$\frac{\text{Force}}{\text{Volume}}.$
✓
Answer
-
$\frac{\text{Force}}{\text{ Area}}.$
-
$\frac{\text{Energy}}{\text{Volume}}.$
Explanation:
Let us first express the relation of pressure with other physical quantities one by one with the help of dimensional analysis.
We know that pressure,
- $\frac{\text{Force}}{\text{Area}}=\frac{[\text{MLT}^{-2}]}{[\text{L}^2]}=[\text{ML}^{-1}\text{T}^{-2}]$
So, this ratio express pressure (In fact this ratio actually represents pressure).
- $\frac{\text{Energy}}{\text{Area}}=\frac{[\text{ML}^{2}\text{T}^{-2}]}{[\text{L}^2]}=[\text{MT}^{-2}]$
Dimensions of this ratio are not same as pressure, so this ratio does not express pressure.
- $\frac{\text{Energy}}{\text{Volume}}=\frac{[\text{ML}^{2}\text{T}^{-2}]}{[\text{L}^3]}=[\text{ML}^{-1}\text{T}^{-2}]$
Dimensions of this ratio is the same as pressure, so this ratio also express pressure.
- $\frac{\text{Force}}{\text{Volume}}=\frac{[\text{ML}\text{T}^{-2}]}{[\text{L}^3]}=[\text{ML}^{-2}\text{T}^{-2}]$
Dimensions of this ratio are not same as pressure, so this ratio does not express pressure.
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