MHT CET · Physics · Units and Dimensions
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 \(\left[\mathrm{L}^{1} \mathrm{M}^{1} \mathrm{~T}^{3} \mathrm{~K}^{-3}\right]\)
- D \(\left[\mathrm{L}^{1} \mathrm{M}^{1} \mathrm{~T}^{-3} \mathrm{~K}^{-3}\right]\)
Answer & Solution
Correct Answer
(D) \(\left[\mathrm{L}^{1} \mathrm{M}^{1} \mathrm{~T}^{-3} \mathrm{~K}^{-3}\right]\)
Step-by-step Solution
Detailed explanation
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,
\([b]=[\lambda][T]=[L K]\)
\(\begin{array}{l}
\therefore \text { Dimensions of }[\sigma b]=\left[M T^{-3} K^{-4}\right][L K] \\
=\left[L^{1} M^{1} T^{-3} K^{-3}\right]
\end{array}\)
\(\begin{array}{l}
{[\sigma]=\frac{[u]}{[\mathrm{A}][\mathrm{T}]^{4}}} \\
=\frac{\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right] /[\mathrm{T}]}{\left[\mathrm{L}^{2} \mathrm{~K}^{4}\right]} \\
=\left[\mathrm{MT}^{-3} \mathrm{~K}^{-4}\right]
\end{array}\)
Dimensions of Wien's constant,
\([b]=[\lambda][T]=[L K]\)
\(\begin{array}{l}
\therefore \text { Dimensions of }[\sigma b]=\left[M T^{-3} K^{-4}\right][L K] \\
=\left[L^{1} M^{1} T^{-3} K^{-3}\right]
\end{array}\)
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