The electrical resistance $R$ of a conductor of length $l$ and area of cross section $a$ is given by $R = \frac{{\rho l}}{a}$ where $\rho$ is the electrical resistivity. What is the dimensional formula for electrical conductivity $\sigma $ which is reciprocal of resistivity?

Time $(T)$, velocity $(C)$ and angular momentum $(h)$ are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be

Write principle of Homogeneity of dimension.

The Bernoulli's equation is given by $p +\frac{1}{2} \rho v ^{2}+ h \rho g = k$

where $p =$ pressure, $\rho =$ density, $v =$ speed, $h =$ height of the liquid column, $g=$ acceleration due to gravity and $k$ is constant. The dimensional formula for $k$ is same as that for

A dimensionless quantity is constructed in terms of electronic charge $e$, permittivity of free space $\varepsilon_0$, Planck's constant $h$, and speed of light $c$. If the dimensionless quantity is written as $e^\alpha \varepsilon_0^\beta h^7 c^5$ and $n$ is a non-zero integer, then $(\alpha, \beta, \gamma, \delta)$ is given by