JEE Main 2022 · 26 Jun · Shift 1 · Physics Q31

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PhysicsSingle correct+4 / -1Question 31 of 90

An expression for a dimensionless quantity P is given by $P=\dfrac\alpha\beta\log_e\left(\dfrac{kt}{\beta x}\right)$ ; where $\alpha$ and $\beta$ are constants, $x$ is distance; k is Boltzmann constant and t is the temperature. Then the dimensions of $\alpha$ will be :

[M^0L^{-1}T^0]

[ML^0T^{-2}]

[MLT^{-2}]

[ML^2T^{-2}]

Answer and worked solution

Official answer: C

Log argument is dimensionless. $\beta=\dfrac{kt}x$ ; $kt$ is an energy, so $[\beta]=\dfrac{ML^2T^{-2}}L=MLT^{-2}$ .

P is dimensionless, so $[\alpha]=[\beta]=MLT^{-2}$ .

(C)

Topics:Dimensional analysis

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JEE Main 2022 · 26 Jun · Shift 1, Physics question 31