Q136 / 150 · MHT CET 2020 (19 Oct Shift 2) · Physics

Let '\sigma' and 'b' be Stefan's constant and Wien's constant respectively, then dimensions of ' $\sigma \mathrm{b}$ ' are

  • A
    $\left[\mathrm{L}^{1} \mathrm{M}^{-1} \mathrm{~T}^{-3} \mathrm{~K}^{-3}\right]$
  • B
    $\left[\mathrm{L}^{-1} \mathrm{M}^{1} \mathrm{~T}^{-3} \mathrm{~K}^{-3}\right]$
  • C
    $\left[\mathrm{L}^{1} \mathrm{M}^{1} \mathrm{~T}^{3} \mathrm{~K}^{-3}\right]$
  • Correct answer
    D
    $\left[\mathrm{L}^{1} \mathrm{M}^{1} \mathrm{~T}^{-3} \mathrm{~K}^{-3}\right]$

Solution

Dimensions of Stefan's constant, $\begin{array}{l} {[\sigma]=\frac{[u]}{[\mathrm{A}][\mathrm{T}]^{4}}} \\ =\frac{\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right] /[\mathrm{T}]}{\left[\mathrm{L}^{2} \mathrm{~K}^{4}\right]} \\ =\left[\mathrm{MT}^{-3} \mathrm{~K}^{-4}\right] \end{array}$ Dimensions of Wien's constant, $[b]=[\lambda][T]=[L K]$ $\begin{array}{l} \therefore \text { Dimensions of }[\sigma b]=\left[M T^{-3} K^{-4}\right][L K] \\ =\left[L^{1} M^{1} T^{-3} K^{-3}\right] \end{array}$

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

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