Q112 / 150 · MHT CET 2020 (14 Oct Shift 1) · Physics

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
    $\left[\mathrm{L}^{0} \mathrm{M}^{1} \mathrm{~T}^{0}\right]$
  • Correct answer
    D
    $\left[\mathrm{L}^{0} \mathrm{M}^{0} \mathrm{~T}^{1}\right]$

Solution

We know that; Dimensional formula of $\mathrm{L}=\mathrm{ML}^{2} \mathrm{~T}^{-2} \mathrm{~A}^{-2}$ Dimensional formula for $\mathrm{R}=\mathrm{R}=\mathrm{ML}^{2} \mathrm{~T}^{-3} \mathrm{~A}^{-2}$ $\frac{\mathrm{L}}{\mathrm{R}}=\frac{\mathrm{ML}^{2}}{\mathrm{~T}^{2} \mathrm{~A}^{2}} \times \frac{\mathrm{T}^{2} \mathrm{~A}^{2}}{\mathrm{ML}^{2}}=\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}$

Hence, the correct answer is option: 'D'.

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