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 𝑎 has dimensions of 𝐼. Quantity 𝑏 has dimensions of 𝐼𝑇. What are the dimensions of 𝑎𝑏?

  • A𝐼𝑇
  • B𝑇
  • C𝑇
  • D𝐼𝑇
  • E𝐼𝑇

Q2:

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

  • A𝑀𝐿𝑇
  • B𝑀𝐿𝑇
  • C𝑀𝐿𝑇
  • D𝑀𝐿𝑇
  • E𝑀𝐿𝑇

Q3:

Quantity 𝑎 has dimensions of 𝐼𝑇. Quantity 𝑏 has dimensions of 𝑇𝑀. What are the dimensions of 𝑎×𝑏?

  • A𝐼𝑀
  • B𝐼𝑇𝑀
  • C𝐼𝑇𝑀
  • D𝐼𝑇𝑀
  • E𝐼𝑀

Q4:

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

  • A𝑀𝐿𝑇
  • B𝑀𝐿𝑇
  • C𝑀𝐿𝑇
  • D𝑀𝑇
  • E𝑀𝐿𝑇

Q5:

Consider the four quantities: 𝑔, 𝐻, 𝑚, and 𝑘, where [𝑔]=𝑀𝐿𝑇, [𝐻]=𝑀𝐿, and [𝑚]=𝑀𝑇.

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

  • A𝑀𝐿
  • B𝑀𝐿𝑇
  • C𝑀𝐿
  • D𝑇𝑀𝐿
  • E𝐿𝑀

Q6:

What are the dimensions of area?

  • A𝐿
  • B𝐿
  • C𝑀
  • D𝑀
  • E𝐿

Q7:

Quantity 𝑎 has dimensions of 𝐼𝑇. Quantity 𝑏 has dimensions of 𝑇. What are the dimensions of 𝑎×𝑏?

  • A𝐼𝑇
  • B𝐼𝑇
  • C𝐼
  • D𝐼𝑇
  • E𝐼𝑇

Q8:

What is the physical quantity that has dimensions of 𝐿𝑇?

  • ADisplacement
  • BVelocity
  • CAcceleration
  • DFrequency
  • EAngular frequency

Q9:

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

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

Q10:

Quantity 𝑎 has dimensions of 𝑀𝐿𝐼. Quantity 𝑏 has dimensions of 𝑇𝐿. What are the dimensions of 𝑎𝑏?

  • A𝑀𝐿𝑇𝐼
  • B𝑀𝐿𝑇𝐼
  • C𝑀𝑇𝐼
  • D𝑀𝑇𝐼
  • E𝑀𝐿𝑇𝐼

Q11:

What are the dimensions of a quantity that can be measured in units of kg⋅m2?

  • A𝑀𝐿
  • B𝑀𝐿
  • C𝑀𝐿
  • D𝑀𝐿
  • E𝑀𝐿

Q12:

Quantity 𝑎 has dimensions of 𝑀. Quantity 𝑏 has dimensions of 𝐿𝑇. Quantity 𝑐 has dimensions of 𝑇. What are the dimensions of 𝑎𝑏𝑐?

  • A𝑀𝐿𝑇
  • B𝑀𝐿
  • C𝑀𝐿
  • D𝑀𝐿
  • E𝑀𝐿𝑇

Q13:

Consider four quantities 𝑝, 𝑞, 𝑅, and 𝑘, where [𝑝]=𝐼𝑇𝐿,[𝑞]=𝐼𝑇𝑀,[𝑅]=𝐿𝑀𝑇. The compound quantity 𝑘𝑝𝑞𝑅 is dimensionless. What are the dimensions of 𝑘?

  • A𝐼𝑇𝐿
  • B𝐼𝑇𝐿𝑀
  • C𝑇𝐿
  • D𝐼𝑇𝐿𝑀
  • E𝑇𝐿

Q14:

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

  • A𝑀𝐿𝑇
  • B𝑀𝐿𝑇
  • C𝑀𝐿𝑇
  • D𝑀𝐿𝑇
  • E𝑀𝐿𝑇

Q15:

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

  • A𝑀𝐿𝑇
  • B𝑀𝐿𝑇
  • C𝑀𝐿𝑇
  • D𝑀𝐿𝑇
  • E𝑀𝐿𝑇

Q16:

Consider three quantities 𝑎, 𝑏, and 𝑐, where [𝑎]=𝑀𝐿 and [𝑏]=𝑀. If 𝑎=𝑏𝑐, what is [𝑐]?

  • A𝑀𝐿
  • B𝑀𝐿
  • C𝑀𝐿
  • D𝐿
  • E𝐿

Q17:

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

  • A𝐿
  • B𝐿
  • C𝐿
  • D𝐿
  • E𝐿

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