Question

Which of the following does not have the same dimension?

• A. Pressure, stress, Youngs modulus
• B. Heat, Potential energy, Work done
• C. Electric flux, Electric field, Electric dipole moment
• D. Electromotive force, Potential difference, Electric voltage

Answer 1

Answer: (C)

B) Pressure: $\frac{force}{Area}$

Stress : $\frac{force}{Area}$

Youngs modulus : $\frac{stress}{strain}$, here strain is dimension less So, all three has same dimension.

C) Electromotive force: $\frac{Energy}{charge}$

Potential difference: $\frac{W}{Q}$, with is same as Electromotive

Electric voltage: If you see in a capacitor, then Voltage is given by $\frac{Energy}{charge}$

D) Heat: $M{L}^2{T}^{-2}$

Potential energy: $mgh\Rightarrow M{L}^2{T}^{-2}$

Work done $=f.d\Rightarrow M{L}^2{T}^{-2}$

A) Electric flux: $M^{-2}SA$

Electric field: $M^2{S}^{-3}{A}^{-1}$

Hence, it has quantities with different units.