Question:
Which pair of physical quantities have same dimensional formula?
Which pair of physical quantities have same dimensional formula?
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Stress, pressure and modulus of elasticity have the same dimensional formula \(ML^{-1}T^{-2}\).
Updated On: May 7, 2026
- Torque and momentum
- Surface tension and tension
- Pressure and modulus of elasticity
- Force constant and Planck's constant
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The Correct Option is C
Solution and Explanation
Concept:
Two physical quantities have the same dimensional formula when they are expressed using the same powers of mass, length and time.
Step 1: Pressure is defined as force per unit area: \[ P=\frac{F}{A} \]
Step 2: Dimension of force is: \[ [F]=MLT^{-2} \]
Step 3: Dimension of area is: \[ [A]=L^2 \]
Step 4: Therefore, dimension of pressure is: \[ [P]=\frac{MLT^{-2}}{L^2}=ML^{-1}T^{-2} \]
Step 5: Modulus of elasticity is defined as: \[ \text{Modulus}=\frac{\text{stress}}{\text{strain}} \]
Step 6: Strain is dimensionless, and stress has the same dimension as pressure. \[ [\text{Modulus of elasticity}]=ML^{-1}T^{-2} \]
Step 7: Hence pressure and modulus of elasticity have the same dimensional formula. \[ \boxed{\text{Pressure and modulus of elasticity}} \]
Two physical quantities have the same dimensional formula when they are expressed using the same powers of mass, length and time.
Step 1: Pressure is defined as force per unit area: \[ P=\frac{F}{A} \]
Step 2: Dimension of force is: \[ [F]=MLT^{-2} \]
Step 3: Dimension of area is: \[ [A]=L^2 \]
Step 4: Therefore, dimension of pressure is: \[ [P]=\frac{MLT^{-2}}{L^2}=ML^{-1}T^{-2} \]
Step 5: Modulus of elasticity is defined as: \[ \text{Modulus}=\frac{\text{stress}}{\text{strain}} \]
Step 6: Strain is dimensionless, and stress has the same dimension as pressure. \[ [\text{Modulus of elasticity}]=ML^{-1}T^{-2} \]
Step 7: Hence pressure and modulus of elasticity have the same dimensional formula. \[ \boxed{\text{Pressure and modulus of elasticity}} \]
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