Dimensional Analysis Quiz: Test Your Physics Unit Skills

1. Density has SI units of kg/m____.

Concept: Density units. Density is mass per volume. Volume uses cubic metres, so the unit is kg/m³.

Explanation

Concept: Density units. Density is mass per volume. Volume uses cubic metres, so the unit is kg/m³.

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2. Writing units clearly at each step is a practical way to avoid mistakes in conversions and formulas.

True

False

Concept: Unit tracking. Units act like a built-in error-checking system. If units don’t cancel or match at the end, something likely went wrong.

Explanation

Concept: Unit tracking. Units act like a built-in error-checking system. If units don’t cancel or match at the end, something likely went wrong.

3. Which is the correct SI unit for frequency?

N

J

W

Hz

Concept: Frequency unit. Frequency counts events per second, so it is measured in hertz (Hz). In base units, Hz = s⁻¹.

Explanation

Concept: Frequency unit. Frequency counts events per second, so it is measured in hertz (Hz). In base units, Hz = s⁻¹.

4. A watt (W) equals kg·m²/s____ in base units.

Concept: Watt in base units. Since W = J/s and J = kg·m²/s², dividing by s gives kg·m²/s³. This helps identify power terms.

Explanation

Concept: Watt in base units. Since W = J/s and J = kg·m²/s², dividing by s gives kg·m²/s³. This helps identify power terms.

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5. Which quantity has units of m²/s²?

Speed

Acceleration

Specific energy (energy per mass)

Pressure

Concept: Energy per mass dimensions. Joule per kilogram is (kg·m²/s²)/kg = m²/s². This appears in contexts like kinetic energy per unit mass.

Explanation

Concept: Energy per mass dimensions. Joule per kilogram is (kg·m²/s²)/kg = m²/s². This appears in contexts like kinetic energy per unit mass.

6. Momentum and impulse have the same dimensions.

True

False

Concept: Impulse–momentum link. Momentum is kg·m/s, and impulse is N·s = (kg·m/s²)·s = kg·m/s. Matching units supports the impulse–momentum relationship.

Explanation

Concept: Impulse–momentum link. Momentum is kg·m/s, and impulse is N·s = (kg·m/s²)·s = kg·m/s. Matching units supports the impulse–momentum relationship.

7. The SI unit of impulse (force × time) is:

N/m

J/s

N·s

Pa·s

Concept: Impulse units. Impulse equals force multiplied by time. That gives units N·s, which also matches change in momentum.

Explanation

Concept: Impulse units. Impulse equals force multiplied by time. That gives units N·s, which also matches change in momentum.

8. Which has the same dimensions as energy?

Force / distance

Pressure / volume

Force × distance

Power × distance

Concept: Energy dimensions. Energy is work, and work is force times distance. That’s why N·m corresponds to joules.

Explanation

Concept: Energy dimensions. Energy is work, and work is force times distance. That’s why N·m corresponds to joules.

9. Converting all quantities to SI base units can help catch mistakes in multi-step problems.

True

False

Concept: Base-unit checking. Base units make dimensions explicit and comparable. This reduces hidden conversion errors and helps verify formulas.

Explanation

Concept: Base-unit checking. Base units make dimensions explicit and comparable. This reduces hidden conversion errors and helps verify formulas.

10. Which equation is dimensionally consistent for speed?

Speed = distance × time

Speed = distance / time

Speed = time / distance

Speed = mass / time

Concept: Speed dimensions. Speed must have dimensions of length per time. Dividing distance by time gives m/s.

Explanation

Concept: Speed dimensions. Speed must have dimensions of length per time. Dividing distance by time gives m/s.

11. Dimensional analysis is mainly used to:

Make graphs look nicer

Check whether an equation’s units are consistent

Replace experiments entirely

Measure temperature more accurately

Concept: Dimensional analysis purpose. It checks whether both sides of an equation have the same dimensions. This can catch mistakes even when you don’t know the correct numbers.

Explanation

Concept: Dimensional analysis purpose. It checks whether both sides of an equation have the same dimensions. This can catch mistakes even when you don’t know the correct numbers.

12. Which expression has the units of power?

Force × distance

Pressure × area

Energy / time

Mass × length

Concept: Power definition. Power is the rate of doing work or transferring energy. So energy divided by time gives watts.

Explanation

Concept: Power definition. Power is the rate of doing work or transferring energy. So energy divided by time gives watts.

13. If the units on both sides match, the equation must be physically correct.

True

False

Concept: Dimensional check is necessary, not sufficient. Matching dimensions is required, but not enough to guarantee correctness. You can still have missing factors or incorrect physics with consistent units.

Explanation

Concept: Dimensional check is necessary, not sufficient. Matching dimensions is required, but not enough to guarantee correctness. You can still have missing factors or incorrect physics with consistent units.

14. The unit 'kg·m/s²' is equivalent to:

Pascal (Pa)

Newton (N)

Joule (J)

Watt (W)

Concept: Newton identification. Force is kg·m/s². That is exactly the definition of the newton.

Explanation

Concept: Newton identification. Force is kg·m/s². That is exactly the definition of the newton.

15. Which is a correct base-unit breakdown of pressure?

Kg·m/s²

Kg/(m·s²)

M²/s

Kg·m²/s³

Concept: Pascal in base units. Pressure is Pa = N/m², and N = kg·m/s². So Pa = (kg·m/s²)/m² = kg/(m·s²).

Explanation

Concept: Pascal in base units. Pressure is Pa = N/m², and N = kg·m/s². So Pa = (kg·m/s²)/m² = kg/(m·s²).

16. Velocity and speed have the same SI units.

True

False

Concept: Units vs vectors. Speed and velocity both use m/s. The difference is that velocity includes direction, but the unit is the same.

Explanation

Concept: Units vs vectors. Speed and velocity both use m/s. The difference is that velocity includes direction, but the unit is the same.

17. If force is N and distance is m, then force × distance has units of:

N/m

J

Pa

W

Concept: Work units. Work is force times distance, and its unit is joule. Since J = N·m, the units match.

Explanation

Concept: Work units. Work is force times distance, and its unit is joule. Since J = N·m, the units match.

18. Acceleration has SI units of m/s____.

Concept: Acceleration units. Acceleration is change in velocity per time. Since velocity is m/s, dividing by another second gives m/s².

Explanation

Concept: Acceleration units. Acceleration is change in velocity per time. Since velocity is m/s, dividing by another second gives m/s².

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19. Which pair can be added directly?

3 m + 2 s

5 n + 1 j

4 cm + 0.02 m

2 kg + 6 a

Concept: Compatible units. Centimetres and metres are both length, so they can be converted and added. Newtons and joules are different physical dimensions.

Explanation

Concept: Compatible units. Centimetres and metres are both length, so they can be converted and added. Newtons and joules are different physical dimensions.

20. You can add two quantities only if they have the same units (or same dimensions).

True

False

Concept: Addition requires same dimensions. Adding unlike units (like metres + seconds) is meaningless in physics. Dimensional analysis helps enforce this rule.

Explanation

Concept: Addition requires same dimensions. Adding unlike units (like metres + seconds) is meaningless in physics. Dimensional analysis helps enforce this rule.