Multiple Choice
Which of the following pairs of terms is mismatched in terms of their dimensional analysis?
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1. Intro to Physics Units
Dimensional Analysis
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Which of the following terms is correctly matched to its description in the context of dimensional analysis?
A
Velocity - [M^1 L^1 T^-2]
B
Energy - [M^1 L^2 T^-1]
C
Acceleration - [L^1 T^-2]
D
Force - [M^1 L^1 T^-2]
Verified step by step guidance1
Step 1: Understand the concept of dimensional analysis. Dimensional analysis involves checking the consistency of dimensions in physical equations. Each physical quantity is expressed in terms of basic dimensions: Mass (M), Length (L), and Time (T).
Step 2: Recall the dimensional formula for velocity. Velocity is defined as the rate of change of displacement with respect to time. Its dimensional formula is [L^1 T^-1], as it involves length per unit time.
Step 3: Recall the dimensional formula for energy. Energy, such as kinetic energy, is expressed as 1/2 mv^2, where m is mass and v is velocity. Its dimensional formula is [M^1 L^2 T^-2], as it involves mass times velocity squared.
Step 4: Recall the dimensional formula for acceleration. Acceleration is the rate of change of velocity with respect to time. Its dimensional formula is [L^1 T^-2], as it involves velocity per unit time.
Step 5: Recall the dimensional formula for force. Force is defined by Newton's second law as mass times acceleration. Its dimensional formula is [M^1 L^1 T^-2], as it involves mass times acceleration.
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