Question 124: Units , Dimensions and Error Analysis

Question

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 :

Accepted Answer

$$u = {\alpha  \over \beta }\sin \left( {{{\alpha x} \over {kt}}} ight)$$
$$[\alpha] = \left[ {{{kt} \over x}} ight] = {{[Energy]} \over {[Dis	an ce]}}$$
$$[\beta ] = {{[\alpha ]} \over {[u]}}$$
$$ = {{[Energy]/[Dis	an ce]} \over {[Energy]/[Volume]}}$$
$$ = [{L^2}]$$

Answer

$$\left[\mathrm{ML}^{2} \mathrm{~T}^{-2} 	heta^{-1}ight]$$

Answer

$$\left[\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{-2}\right]$$

Answer

$$\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0}\right]$$

Answer

$$\left[\mathrm{M}^{0} \mathrm{~L}^{2} \mathrm{~T}^{0}\right]$$

Units , Dimensions and Error Analysis

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 :

Choose the correct answer: