# 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 ?

• BVelocity
• CAcceleration
• DFrequency
• EAngular frequency

Q9:

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

• Am/s2
• Bm⋅s2
• Cm/s
• Dm⋅s
• Em2⋅s2

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⋅m2?

• 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