Question

Match List-I with List-II. \[ \begin{array}{|c|c|} \hline \text{List-I} & \text{List-II}
\hline

• A. \text{Permeability of free space} & (I) \left[ \text{M L}^2 \text{T}^{-2} \right]
• B. \text{Magnetic field} & (II) \left[ \text{M T}^{-2} \text{A}^{-1} \right]
• C. \text{Magnetic moment} & (III) \left[ \text{M L T}^{-2} \text{A}^{-2} \right]
• D. \text{Torsional constant} & (IV) \left[ \text{L}^2 \text{A} \right] \hline \end{array} \] Choose the correct answer from the options given below:

Hint:

In dimensional analysis, match the physical quantities with their corresponding dimensions based on the units involved.

Answer 1

The Correct Option is D

Permeability of free space $\mu_0$ has the dimensional formula $[M L^3 T^{-4} A^{-2}]$.
- Magnetic field $B$ has the dimensional formula $[M T^{-2} A^{-1}]$.
- Magnetic moment $M$ has the dimensional formula $[M L T^{-2} A^{-2}]$.
- Torsional constant has the dimensional formula $[L^2 A]$. Thus, the correct matching is: $$(A)-(III), (B)-(II), (C)-(IV), (D)-(I).$$