Which of the following terms has different dimension from the others?

Analyze the question: We need to find the quantity whose dimension differs from the rest. So we find the dimensions of each option.

Key concepts:

• Stress = Force/Area, so its dimension is MLT⁻² / L² = ML⁻¹T⁻²
• Strain = change in length/original length, so it is dimensionless
• Pressure = Force/Area, so its dimension is ML⁻¹T⁻²
• Torque = Force × perpendicular distance, so its dimension is MLT⁻² × L = ML²T⁻²

Step by step:

• A. Stress × Strain = ML⁻¹T⁻² × 1 = ML⁻¹T⁻²
• B. Pressure = ML⁻¹T⁻²
• C. Stress/Strain (this is Young's modulus) = ML⁻¹T⁻² ÷ 1 = ML⁻¹T⁻²
• D. Torque = ML²T⁻²

Options A, B and C all have the dimension ML⁻¹T⁻². Only torque (D) has ML²T⁻², which is the same as the dimension of energy or work.

Answer: D

Tip: Strain is dimensionless, so multiplying or dividing by it never changes the dimension. Also remember that pressure, stress and Young's modulus all share ML⁻¹T⁻², while torque and energy share ML²T⁻². Torque and work have the same dimension even though they are different physical quantities.