Question

The set of physical quantities among the following which are dimensionally different is

• A. Terminal velocity, drift velocity, critical velocity
• B. Potential energy, work done, kinetic energy
• C. Pressure, stress, rigidity modulus
• D. Disintegration constant, frequency, angular velocity
• E. Dipole moment, electric flux, electric field

Hint:

Always reduce to fundamental dimensions before comparing.

Answer 1

Answer: (E)

Concept: Dimensional analysis
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Step 1: Check each option --- (A) Velocities: \[ [L T^{-1}] \quad \text{(all same)} \Rightarrow \text{Not correct} \] --- (B) Energy: \[ [M L^2 T^{-2}] \quad \text{(all same)} \Rightarrow \text{Not correct} \] --- (C) Pressure, stress, modulus: \[ [M L^{-1} T^{-2}] \quad \text{(all same)} \Rightarrow \text{Not correct} \] --- (D) Frequency, angular velocity: \[ [T^{-1}] \quad \text{(all same)} \Rightarrow \text{Not correct} \] --- (E) Check individually: Dipole moment: \[ [q \cdot d] = [I T \cdot L] \] Electric flux: \[ [E \cdot A] = [M L T^{-3} I^{-1} \cdot L^2] \] Electric field: \[ [M L T^{-3} I^{-1}] \] All are different. --- Final Answer: \[ \boxed{\text{Option E}} \]