Practice Dimensional Reasoning in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Using the units and dimensions of physical quantities to check formulas, guide derivations, and eliminate impossible answers.
Units must balance on both sides of any physical equation — if the units do not match, the formula is wrong regardless of the numbers.
Example 1
easyUse dimensional analysis to find the units of pressure, given that pressure = \text{force}/\text{area}, force is in Newtons (\text{kg}\cdot\text{m}/\text{s}^2), and area is in m².
Example 2
mediumA formula for the period of a pendulum is proposed as T = 2\pi\sqrt{L/g} where L is length (m) and g is gravitational acceleration (m/s²). Verify dimensional consistency.
Example 3
easyConvert 60 km/h to m/s using dimensional analysis.
Example 4
mediumA student writes E = mc for Einstein's mass-energy formula. Use dimensional reasoning to explain why this cannot be correct and what the correct formula should be.