Q.(MCQ II — one or more options correct) Which of the following ratios express pressure?

The key idea is that pressure is defined as force per unit area. We check each option by reducing it to base SI units.

• (A) Force/Area — This is the direct definition of pressure. Correct.
• (B) Energy/Volume — Energy is $[M L^2 T^{-2}]$, volume is $[L^3]$, so $\frac{[M L^2 T^{-2}]}{[L^3]} = [M L^{-1} T^{-2}]$, which matches pressure. Correct.
• (C) Energy/Area — $\frac{[M L^2 T^{-2}]}{[L^2]} = [M T^{-2}]$, which is not pressure. Incorrect. …

Pressure is defined as the perpendicular force applied per unit area. Its SI unit is the pascal (Pa), which equals one newton per square metre. But in physics problems, especially multiple-choice questions with multiple correct options, you often need to check which combinations of physical quantities yield the same dimensions as pressure. The most reliable tool here is dimensional analysis — comparing the fundamental dimensions (mass $M$, length $L$, time $T$) of each expression.

Let’s recall the dimension of pressure first.

Force has dimensions $[M L T^{-2}]$, and area has $[L^2]$. So:

That’s our target dimension. Now we check each option.

1. Option (A): Force/Area

   This is exactly the definition of pressure. Its dimension is $[M L^{-1} T^{-2}]$. So (A) is correct.

2. Option (B): Energy/Volume

   Energy (work) has dimensions of force times distance: $[M L^2 T^{-2}]$. Volume is $[L^3]$. Dividing:

This matches pressure exactly. So (B) is also correct.

3. Option (C): Energy/Area …

Concept: Dimensional Analysis of Pressure

Pressure is defined as force per unit area. Its dimensional formula is:

We will check each option by deriving its dimensions.

Method: Dimensional Verification

Step 1 — Write dimensions of base quantities

• Force: $[F] = [M L T^{-2}]$
• Area: $[A] = [L^2]$
• Volume: $[V] = [L^3]$
• Energy (work): $[E] = [M L^2 T^{-2}]$

Step 2 — Check each option

(A) Force/Area

✓ Matches pressure.

(B) Energy/Volume

$\frac{[E]}{[V]} = \frac{[M L^2 T^{-2}]}{[L^3]} = [M L^{-1} T^{-2}]$ …

Common Mistakes & How to Avoid Them

Mistake 1: Selecting only (A) and missing (B)

Why students do this:

Most students memorise that Pressure = Force/Area. So they tick (A) and stop. They don't check whether other options can be rearranged to give the same dimensions.

How to avoid:

Always check dimensions of every option — even if it looks unfamiliar.

• Pressure $[P] = [M L^{-1} T^{-2}]$
• Energy $[E] = [M L^2 T^{-2}]$
• Volume $[V] = [L^3]$
• So $\frac{\text{Energy}}{\text{Volume}} = \frac{[M L^2 T^{-2}]}{[L^3]} = [M L^{-1} T^{-2}]$ → same as pressure ✓

Key rule: If you can rewrite a quantity as Force/Area, it is pressure. Energy/Volume = (Force × Distance)/Volume = Force/Area.

Mistake 2: Thinking (C) Energy/Area is also pressure

Why students do this:

They see "Energy" and "Area" and think: "Energy/Volume worked, so Energy/Area should also work." This is a hasty generalisation.

How to avoid:

Do the dimensional check:

• $\frac{\text{Energy}}{\text{Area}} = \frac{[M L^2 T^{-2}]}{[L^2]} = [M T^{-2}]$
• This is not $[M L^{-1} T^{-2}]$ → not pressure ✗

Memory tip: Pressure always has $L^{-1}$ in its dimension. Energy/Area has no $L^{-1}$ — it's missing the "per unit length" factor.

Mistake 3: Selecting (D) Force/Volume

Why students do this:

They confuse "Force/Volume" with "Force/Area". The words look similar, but the dimensions are different.

How to avoid:

• Force/Volume = $\frac{[M L T^{-2}]}{[L^3]} = [M L^{-2} T^{-2}]$
• This is pressure gradient (change in pressure per unit length), not pressure ✗

Quick check: Pressure is force per unit area ($L^2$), not per unit volume ($L^3$).

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