Pressure is defined as force per unit area. The dimensional formula for force is M¹L¹T⁻², and for area is L², thus pressure = M¹L¹T⁻² / L² = M¹L⁻¹T⁻².
Questions & Step-by-step Solutions
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Q: What is the dimensional formula for pressure?
Solution: Pressure is defined as force per unit area. The dimensional formula for force is M¹L¹T⁻², and for area is L², thus pressure = M¹L¹T⁻² / L² = M¹L⁻¹T⁻².
Steps: 7
Step 1: Understand that pressure is defined as force divided by area.
Step 2: Write the formula for pressure: Pressure = Force / Area.
Step 3: Find the dimensional formula for force. Force is mass times acceleration, which is M (mass) times L (length) divided by T (time) squared. So, the dimensional formula for force is M¹L¹T⁻².
Step 4: Find the dimensional formula for area. Area is length times length, which is L².
Step 5: Substitute the dimensional formulas into the pressure formula: Pressure = (M¹L¹T⁻²) / (L²).
Step 6: Simplify the expression: M¹L¹T⁻² / L² = M¹L¹⁻²T⁻².
Step 7: Write the final dimensional formula for pressure: M¹L⁻¹T⁻².
