Lesson Worksheet: Dimensional Analysis Physics

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

Q1:

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

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

Q2:

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

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

Q3:

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

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

Q4:

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

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

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

This lesson includes 19 additional questions and 64 additional question variations for subscribers.

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