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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.
Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimension of $L$, which of the following statement ($s$) is/are correct ?
$(1)$ The dimension of force is $L ^{-3}$
$(2)$ The dimension of energy is $L ^{-2}$
$(3)$ The dimension of power is $L ^{-5}$
$(4)$ The dimension of linear momentum is $L ^{-1}$