Units And Formulas Quiz: Master Physics Measurement Skills

1. You can check whether a formula is plausible by confirming both sides reduce to the same base units.

True

False

Concept: dimensional consistency check. If base units don’t match, the formula cannot be correct. This is a quick and powerful error check.

Explanation

Concept: dimensional consistency check. If base units don’t match, the formula cannot be correct. This is a quick and powerful error check.

2. If (f = ma), and (a) has units m/s², then force has units:

Kg/s²

Kg·m/s²

M·s/kg

Kg·m²/s

Concept: deriving units from definitions. Multiply mass (kg) by acceleration (m/s²). The product gives kg·m/s², which is the newton.

Explanation

Concept: deriving units from definitions. Multiply mass (kg) by acceleration (m/s²). The product gives kg·m/s², which is the newton.

3. Power is energy per time. If energy is j and time is s, power units are:

J·s

J/s

S/j

N/m

Concept: power units. Power is the rate of energy transfer. Joules per second is the watt (W).

Explanation

Concept: power units. Power is the rate of energy transfer. Joules per second is the watt (W).

4. 1 watt (W) equals 1 joule per ______.

Concept: watt definition. The watt is a derived unit defined by energy per time. It simplifies many energy-rate calculations.

Explanation

Concept: watt definition. The watt is a derived unit defined by energy per time. It simplifies many energy-rate calculations.

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5. If (v = d/t), then (d = vt) has units:

M/s

M

S

M/s²

Concept: unit propagation. Velocity (m/s) times time (s) gives meters. Units multiply and cancel just like algebraic symbols.

Explanation

Concept: unit propagation. Velocity (m/s) times time (s) gives meters. Units multiply and cancel just like algebraic symbols.

6. Units can be treated like algebra: you can multiply, divide, and cancel them.

True

False

Concept: unit algebra. Dimensional analysis works because units follow consistent multiplication/division rules. Cancelling units helps confirm the final unit.

Explanation

Concept: unit algebra. Dimensional analysis works because units follow consistent multiplication/division rules. Cancelling units helps confirm the final unit.

7. Momentum has units:

Kg·m²/s²

Kg·m/s

N/s

M/s²

Concept: momentum units. Momentum is mass times velocity. That gives kg·m/s.

Explanation

Concept: momentum units. Momentum is mass times velocity. That gives kg·m/s.

8. Impulse (force × time) has the same units as momentum.

True

False

Concept: impulse–momentum link. Force (kg·m/s²) times time (s) gives kg·m/s. That matches momentum, consistent with impulse changing momentum.

Explanation

Concept: impulse–momentum link. Force (kg·m/s²) times time (s) gives kg·m/s. That matches momentum, consistent with impulse changing momentum.

9. Which is dimensionally correct for kinetic energy?

E_k = mv

E_k = ½ m v²

E_k = ½ m² v

E_k = v²/m

Concept: energy dimension check. Energy should have units kg·m²/s². (m v²) gives kg·(m²/s²), which matches.

Explanation

Concept: energy dimension check. Energy should have units kg·m²/s². (m v²) gives kg·(m²/s²), which matches.

10. Constants like 1/2 do not affect dimensions.

True

False

Concept: dimensionless constants. Pure numbers don’t carry units. They can change magnitude but not dimensional consistency.

Explanation

Concept: dimensionless constants. Pure numbers don’t carry units. They can change magnitude but not dimensional consistency.

11. If pressure is pa = n/m² and 1 n = kg·m/s², then pa in base units is:

Kg·m/s²

Kg/(m·s²)

Kg·m²/s²

M/(kg·s²)

Concept: reducing derived units. Substitute n and divide by m²: (kg·m/s²)/m² = kg/(m·s²). That’s the base-unit form of pressure.

Explanation

Concept: reducing derived units. Substitute n and divide by m²: (kg·m/s²)/m² = kg/(m·s²). That’s the base-unit form of pressure.

12. The unit for frequency is hertz (Hz), which equals 1/______.

Concept: frequency as inverse time. Frequency counts cycles per second. Its unit is s⁻¹.

Explanation

Concept: frequency as inverse time. Frequency counts cycles per second. Its unit is s⁻¹.

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13. The equation (s = ut + ½ at²) is dimensionally consistent for displacement (s).

True

False

Concept: checking kinematics equation. (ut) has (m/s)·s = m. (at²) has (m/s²)·s² = m, so both terms match displacement units.

Explanation

Concept: checking kinematics equation. (ut) has (m/s)·s = m. (at²) has (m/s²)·s² = m, so both terms match displacement units.

14. Which term would be dimensionally wrong to add to a length (l)?

3 m

0.2 km

50 cm

4 m/s

Concept: add only same dimensions. m/s is a speed, not a length. You cannot add a speed to a length.

Explanation

Concept: add only same dimensions. m/s is a speed, not a length. You cannot add a speed to a length.

15. If an equation is dimensionally inconsistent, it must be wrong.

True

False

Concept: dimensional inconsistency is fatal. Physical equations must match dimensions on both sides. If they don’t, the relationship cannot be correct.

Explanation

Concept: dimensional inconsistency is fatal. Physical equations must match dimensions on both sides. If they don’t, the relationship cannot be correct.

16. Which quantity has units of m/s²?

Speed

Momentum

Acceleration

Energy

Concept: identifying common units. Acceleration is change in velocity per time. That gives m/s².

Explanation

Concept: identifying common units. Acceleration is change in velocity per time. That gives m/s².

17. In dimensional symbols, speed can be written as (l t^{-1}) and acceleration as (l t^{-2}), where (l) is length and (t) is ______.

Concept: dimensional notation. Dimensional symbols compress unit information into powers. (t) stands for time in this shorthand.

Explanation

Concept: dimensional notation. Dimensional symbols compress unit information into powers. (t) stands for time in this shorthand.

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18. You can often spot a missing square in a formula because the units won’t match.

True

False

Concept: common unit-check catch. Many mistakes involve missing squares on time or speed. Unit mismatch highlights the error immediately.

Explanation

Concept: common unit-check catch. Many mistakes involve missing squares on time or speed. Unit mismatch highlights the error immediately.

19. If energy is measured in joules (j) and 1 j = n·m, then in base units j equals:

Kg·m/s²

Kg·m²/s²

Kg/(m·s²)

M²/s²

Concept: joule in base units. n is kg·m/s², multiply by m gives kg·m²/s². That is the base-unit form of energy.

Explanation

Concept: joule in base units. n is kg·m/s², multiply by m gives kg·m²/s². That is the base-unit form of energy.

20. The best overall use of this level of dimensional analysis is to:

Replace careful experiments

Check units and derive correct units for results

Avoid learning any physics

Decide which colour graph to use

Concept: practical unit-checking. At this level, dimensional analysis is a tool for verifying and deriving units. It keeps calculations consistent and reduces mistakes.

Explanation

Concept: practical unit-checking. At this level, dimensional analysis is a tool for verifying and deriving units. It keeps calculations consistent and reduces mistakes.