MHT CET · Physics · Units and Dimensions
Let the inductance and resistance be denoted by 'L' and 'R' respectively. The dimensions of \(\left(\frac{\mathrm{L}}{\mathrm{R}}\right)\) are
- A \(\left[\mathrm{L}^{1} \mathrm{M}^{0} \mathrm{~T}^{1}\right]\)
- B \(\left[\mathrm{L}^{0} \mathrm{M}^{0} \mathrm{~T}^{0}\right]\)
- C \(\left[\mathrm{L}^{0} \mathrm{M}^{1} \mathrm{~T}^{0}\right]\)
- D \(\left[\mathrm{L}^{0} \mathrm{M}^{0} \mathrm{~T}^{1}\right]\)
Answer & Solution
Correct Answer
(D) \(\left[\mathrm{L}^{0} \mathrm{M}^{0} \mathrm{~T}^{1}\right]\)
Step-by-step Solution
Detailed explanation
We know that;
Dimensional formula of \(\mathrm{L}=\mathrm{ML}^{2} \mathrm{~T}^{-2} \mathrm{~A}^{-2}\)
Dimensional formula for \(\mathrm{R}=\mathrm{R}=\mathrm{ML}^{2} \mathrm{~T}^{-3} \mathrm{~A}^{-2}\)
\(\frac{\mathrm{L}}{\mathrm{R}}=\frac{\mathrm{ML}^{2}}{\mathrm{~T}^{2} \mathrm{~A}^{2}} \times \frac{\mathrm{T}^{2} \mathrm{~A}^{2}}{\mathrm{ML}^{2}}=\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}\)
Dimensional formula of \(\mathrm{L}=\mathrm{ML}^{2} \mathrm{~T}^{-2} \mathrm{~A}^{-2}\)
Dimensional formula for \(\mathrm{R}=\mathrm{R}=\mathrm{ML}^{2} \mathrm{~T}^{-3} \mathrm{~A}^{-2}\)
\(\frac{\mathrm{L}}{\mathrm{R}}=\frac{\mathrm{ML}^{2}}{\mathrm{~T}^{2} \mathrm{~A}^{2}} \times \frac{\mathrm{T}^{2} \mathrm{~A}^{2}}{\mathrm{ML}^{2}}=\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}\)
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