WBJEE · Physics · Units and Dimensions
The Entropy (S) of a black hole can be written as \(S=\beta k_B A\), where \(k_B\) is the Boltzmann constant and \(A\) is the area of the black hole. Then \(\beta\) has dimension of
- A \(\mathrm{L}^2\)
- B \(\quad \mathrm{ML}^2 \mathrm{~T}^{-1}\)
- C \(\mathrm{L}^{-2}\)
- D dimensionless
Answer & Solution
Correct Answer
(C) \(\mathrm{L}^{-2}\)
Step-by-step Solution
Detailed explanation
\(\begin{array}{ll} \mathrm{S}= \beta \mathrm{K}_\beta \mathrm{A} \\ \frac{\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]}{[\theta]}=[\beta]\left[\frac{\mathrm{ML}^2 \mathrm{~T}^{-2}}{\theta}\right]\left[\mathrm{L}^2\right] \quad[\beta]=\left[\mathrm{L}^{-2}\right] \end{array}\)
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