# Worksheet: Dimensional Analysis

In this worksheet, we will practice determining the dimensions of physical quantities given the relation between those quantities and other known quantities.

**Q1: **

Quantity has dimensions of . Quantity has dimensions of . What are the dimensions of ?

- A
- B
- C
- D
- E

**Q2: **

What are the dimensions of a quantity that is equal to a force multiplied by a distance?

- A
- B
- C
- D
- E

**Q3: **

Quantity has dimensions of . Quantity has dimensions of . What are the dimensions of ?

- A
- B
- C
- D
- E

**Q4: **

What are the dimensions of a quantity that is equal to momentum divided by time?

- A
- B
- C
- D
- E

**Q5: **

Consider the four quantities: , , , and , where , , and .

The compound quantity is dimensionless. What are the dimensions of ?

- A
- B
- C
- D
- E

**Q6: **

What are the dimensions of area?

- A
- B
- C
- D
- E

**Q7: **

Quantity has dimensions of . Quantity has dimensions of . What are the dimensions of ?

- A
- B
- C
- D
- E

**Q8: **

What is the physical quantity that has dimensions of ?

- ADisplacement
- BVelocity
- CAcceleration
- DFrequency
- EAngular frequency

**Q9: **

A quantity has dimensions of . What SI unit could this quantity be measured in?

- Am/s
^{2} - Bm⋅s
^{2} - Cm/s
- Dm⋅s
- Em
^{2}⋅s^{2}

**Q10: **

Quantity has dimensions of . Quantity has dimensions of . What are the dimensions of ?

- A
- B
- C
- D
- E

**Q11: **

What are the dimensions of a quantity that can be measured in units of kg⋅m^{2}?

- A
- B
- C
- D
- E

**Q12: **

Quantity has dimensions of . Quantity has dimensions of . Quantity has dimensions of . What are the dimensions of ?

- A
- B
- C
- D
- E

**Q13: **

Consider four quantities , , , and , where The compound quantity is dimensionless. What are the dimensions of ?

- A
- B
- C
- D
- E

**Q14: **

What are the dimensions of a quantity that can be measured in units of N⋅m?

- A
- B
- C
- D
- E

**Q15: **

What are the dimensions of a quantity that can be measured in units of N?

- A
- B
- C
- D
- E

**Q16: **

Consider three quantities , , and , where and . If , what is ?

- A
- B
- C
- D
- E

**Q17: **

What are the dimensions of a quantity that can be measured in units of miles?

- A
- B
- C
- D
- E