An expression of energy density is given by $u=\frac{\alpha}{\beta} \sin \left(\frac{\alpha x}{k t}\right)$, where $\alpha, \beta$ are constants, $x$ is displacement, $k$ is Boltzmann constant and $t$ is the temperature. The dimensions of $\beta$ will be.

Q: An expression of energy density is given by $u=\frac{\alpha}{\beta} \sin \left(\frac{\alpha x}{k t}\right)$, where $\alpha, \beta$ are constants, $x$ is displacement, $k$ is Boltzmann constant and $t$ is the temperature. The dimensions of $\beta$ will be.

d $\frac{\alpha[ L ]}{\left[ ML ^{2} T ^{-2}\right]}=\left[ M ^{0} L ^{0} T ^{0}\right]$ $\alpha=\left[ ML ^{1} T ^{-2}\right]$ $\frac{\alpha}{\beta}=\frac{\left[ ML ^{2} T ^{-2}\right]}{\left[ L ^{3}\right]} \Rightarrow \beta=\frac{\left[ ML ^{1} T ^{-2}\right]\left[ L ^{3}\right]}{ ML ^{2} T ^{-2}}$

Question

A$\left[ ML ^{2} T ^{-2} \theta^{-1}\right]$
B$\left[ M ^{0} L ^{2} T ^{-2}\right]$
C$\left[ M ^{0} L ^{0} T ^{0}\right]$
D$\left[ M ^{0} L ^{2} T ^{0}\right]$

JEE MAIN 2022, Diffcult

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