JEE Mains · Physics · STD 11 - Units,dimensions and measurement
- JEE Mains 2024
- Hard
- MCQ
Match List \(I\) with List \(II\)
| List - \(I\) | List - \(II\) |
| \((A)\) Torque | \((I)\) \({\left[\mathrm{M}^1 \mathrm{~L}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-2}\right]}\) |
| \((B)\) Magnetic fileld | \((II)\) \(\left[\mathrm{L}^2 \mathrm{~A}^1\right]\) |
| \((C)\) Magneti moment | \((III)\) \({\left[\mathrm{M}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]}\) |
| \((D)\) permeability of free space | \((IV)\) \(\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]\) |
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(A-IV, B-III, C-II, D-I\)
Step-by-step Solution
Detailed explanation
\({[\tilde{\tau}]=[\overrightarrow{\mathrm{r}} \times \overrightarrow{\mathrm{F}}]=\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]}\)
\({[\mathrm{F}]=[\mathrm{qVB}]}\)
\(\Rightarrow \mathrm{B}=\left(\frac{\mathrm{F}}{\mathrm{qV}}\right)=\left[\frac{\mathrm{MLT}^{-2}}{\mathrm{ATLT}^{-1}}\right]=\left[\mathrm{MA}^{-1} \mathrm{~T}^{-2}\right]\)
\({[\mathrm{M}]=[\mathrm{I} \times \mathrm{A}]=\left[\mathrm{AL}^2\right]}\)
\(\mathrm{B}=\frac{\mu_0}{4 \pi} \frac{\mathrm{Idl} \sin \theta}{\mathrm{r}^2}\)
\(\Rightarrow[\mu]=\left[\frac{\mathrm{Br}^2}{\mathrm{Idl}}\right]=\left[\frac{\mathrm{MT}^{-2} \mathrm{~A}^{-1} \times \mathrm{L}^2}{\mathrm{AL}}\right]\)
\(=\left[\mathrm{MLT}^{-2} \mathrm{~A}^{-2}\right]\)
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