Multiple Choice
Which of the following physical quantities can be used to determine the length of the base in a dimensional analysis problem?
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1. Intro to Physics Units
Dimensional Analysis
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Which of the following pairings of physical quantities and their dimensions is correct?
A
Force - [M L T^-2]
B
Power - [M L^2 T^-1]
C
Energy - [M L^2 T^-3]
D
Pressure - [M L^-1 T^-2]
Verified step by step guidance1
Understand the concept of dimensions: Dimensions are the powers to which the fundamental units (mass, length, time) are raised to represent a physical quantity.
Recall the formula for Force: Force is defined as mass times acceleration. The dimension of mass is [M], and acceleration is [L T^-2], so the dimension of force is [M L T^-2].
Recall the formula for Power: Power is the rate at which work is done or energy is transferred. Work or energy has the dimension [M L^2 T^-2], and time has the dimension [T], so the dimension of power is [M L^2 T^-3] divided by [T], which simplifies to [M L^2 T^-1].
Recall the formula for Energy: Energy is typically measured in terms of work done, which is force times distance. Force has the dimension [M L T^-2] and distance has the dimension [L], so the dimension of energy is [M L^2 T^-2].
Recall the formula for Pressure: Pressure is defined as force per unit area. Force has the dimension [M L T^-2] and area has the dimension [L^2], so the dimension of pressure is [M L T^-2] divided by [L^2], which simplifies to [M L^-1 T^-2].
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