Dimensional Consistency Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Check: E=mc2E = mc^2 where EE is energy (kg·m²/s²), mm is mass (kg), cc is speed (m/s).

Solution

  1. 1
    Step 1: [mc2]=kg⋅(m/s)2=kg⋅m2/s2[mc^2] = \text{kg} \cdot (\text{m/s})^2 = \text{kg} \cdot \text{m}^2/\text{s}^2.
  2. 2
    Step 2: [E]=kg⋅m2/s2[E] = \text{kg} \cdot \text{m}^2/\text{s}^2 (joules).
  3. 3
    Step 3: Both sides have the same dimensions ✓

Answer

Yes, dimensionally consistent.
Dimensional analysis can verify equations and even derive relationships. If an equation is dimensionally inconsistent, it is definitely wrong (though consistency doesn't guarantee correctness).

About Dimensional Consistency

The principle that every term added or equated in a valid equation must share the same physical dimensions or units.

Learn more about Dimensional Consistency →

More Dimensional Consistency Examples

Example 1 easy

Is the equation [formula] (velocity = distance + time) dimensionally consistent?

Example 3 easy

Is [formula] a valid formula for area?

Example 4 medium

In the equation [formula] (where [formula] is in meters), are all terms dimensionally consistent?

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