Pressure is defined as force per unit area. The dimensions of force are ML^1T^-2, and area is L^2, thus pressure has dimensions ML^-1T^-2.
What are the dimensions of pressure?
Practice Questions
Q1
What are the dimensions of pressure?
ML^-1T^-2
ML^2T^-2
ML^2T^-1
M^0L^0T^0
Questions & Step-by-Step Solutions
What are the dimensions of pressure?
Correct Answer: ML^-1T^-2
Step 1: Understand that pressure is defined as force divided by area.
Step 2: Know the formula for pressure: Pressure = Force / Area.
Step 3: Identify the dimensions of force. Force is measured in mass (M) times acceleration (which is length (L) divided by time squared (T^2)). So, the dimensions of force are ML^1T^-2.
Step 4: Identify the dimensions of area. Area is measured in length times length, which gives us L^2.
Step 5: Substitute the dimensions of force and area into the pressure formula: Pressure = (ML^1T^-2) / (L^2).
Step 6: Simplify the dimensions: ML^1T^-2 divided by L^2 equals ML^(1-2)T^-2, which simplifies to ML^-1T^-2.
Step 7: Conclude that the dimensions of pressure are ML^-1T^-2.
Pressure – Pressure is defined as the force applied per unit area.
Dimensions of Force – Force has dimensions of mass (M), length (L), and time (T), specifically ML^1T^-2.
Dimensions of Area – Area is calculated as length squared, giving it dimensions of L^2.
Dimensional Analysis – The process of determining the dimensions of a physical quantity by analyzing its fundamental components.
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