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.
$\left[ ML ^{2} T ^{-2} \theta^{-1}\right]$
$\left[ M ^{0} L ^{2} T ^{-2}\right]$
$\left[ M ^{0} L ^{0} T ^{0}\right]$
$\left[ M ^{0} L ^{2} T ^{0}\right]$
Frequency is the function of density $(\rho )$, length $(a)$ and surface tension $(T)$. Then its value is
The mass of a liquid flowing per second per unit area of cross section of a tube is proportional to $P^x$ and $v^y$ , where $P$ is the pressure difference and $v$ is the velocity. Then, the relation between $x$ and $y$ is
Heat produced in a current carrying conducting wire depends on current $I$, resistance $R$ of the wire and time $t$ for which current is passed. Using these facts, obtain the formula for heat energy.
If time $(t)$, velocity $(u)$, and angular momentum $(I)$ are taken as the fundamental units. Then the dimension of mass $({m})$ in terms of ${t}, {u}$ and ${I}$ is