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Physics Question 37 – NEET-UG 2026

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Consider that σs, kB, b represent Stefan-Boltzmann constant, Boltzmann constant and Wien's displacement law constant, respectively. The dimension of σskB−1b is :

Dimensional analysis involves expressing physical quantities in terms of fundamental dimensions like Mass (M), Length (L), Time (T), and Temperature (K).

Step 1: Determine the dimensions of each constant✦ Active

The dimensions of the given constants are:

Stefan-Boltzmann constant (σs): From P=σsAT4⟹σs=PAT4 [σs]=[M L2T−3][L2][K4]=[M T−3K−4]
Boltzmann constant (kB): From E=kBT⟹kB=ET [kB]=[M L2T−2][K]=[M L2T−2K−1]
Wien's displacement law constant (b): From λmaxT=b [b]=[L][K]=[L K]
💡 Teacher's Secret Hint

Remember the fundamental equations associated with each constant to derive their dimensions accurately.

Step 2: Calculate the dimension of the expression σskB−1b○ Expand

Now, substitute the individual dimensions into the expression:

[σskB−1b]=[σs][kB]−1[b] =([M T−3K−4])([M L2T−2K−1])−1([L K])

Simplify the inverse dimension for kB:

[kB]−1=[M−1L−2T2K1]

Substitute back and combine the exponents for M, L, T, and K:

[σskB−1b]=([M T−3K−4])([M−1L−2T2K1])([L K])

For M: 1+(−1)=0 For L: 0+(−2)+1=−1 For T: (−3)+2=−1 For K: (−4)+1+1=−2

[σskB−1b]=[M0L−1T−1K−2]=[L−1T−1K−2]
💡 Teacher's Secret Hint

Pay close attention to the exponents, especially when dealing with inverse dimensions. A common mistake is to forget to invert all exponents.

Step 3: Match with the given options○ Expand

The calculated dimension [L−1T−1K−2] matches option (1).

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