Dimensional Analysis in Physics

What are the three basic dimensions discussed in the introduction to mechanics?

• Length, mass, and time

• Time, speed, and velocity

• Mass, volume, and density

• Length, width, and height

According to the basic rules of dimensional analysis, what must be true for the dimensions on both sides of an equation?

• They must be different

• They must be inversely related

• They must be equal

• They must be proportional

When adding two terms in an equation, what must be true about their dimensions?

• They must be different

• They must be equal

• They must be negative

• They must be zero

What happens to the dimensions when you multiply two different dimensions together?

• They add up

• They cancel out

• They remain the same

• They form a new dimension

What is the dimension of volume for a rectangular box?

• Time squared

• Mass per length

• Length cubed

• Length squared

How is the dimension of acceleration derived from velocity and time?

• Length per time

• Time per length

• Length per time squared

• Mass per time

In the equation mass = density × volume, what is the dimension of density?

• Mass per length

• Mass per length cubed

• Time per mass

• Length per mass

What is the purpose of using dimensional analysis to check an equation?

• To ensure dimensions are consistent

• To calculate the speed of an object

• To find the exact numerical value

• To determine the mass of an object

In the equation position = velocity × time + 1/2 × acceleration × time squared, what is the dimension of position?

• Length

• Time

• Velocity

• Mass

Why might dimensional analysis not fully verify the correctness of an equation?

• It ignores numerical factors

• It only checks for mass

• It only applies to time

• It requires exact values