Let $l, r, c$ and $v$ represent inductance, resistance, capacitance and voltage, respectively. The dimension of $\frac {l}{rcv}$ in $SI\,units$ will be
$[LA^{-2}]$
$[A^{-1}]$
$[LTA]$
$[LT^2]$
The dimensions of ${\left( {{\mu _0}{\varepsilon _0}} \right)^{ - \frac{1}{2}}}$ are
If force $(F)$, length $(L) $ and time $(T)$ are assumed to be fundamental units, then the dimensional formula of the mass will be
The dimensional formula of wave number is
Consider a simple pendulum, having a bob attached to a string, that oscillates under the action of the force of gravity. Suppose that the period of oscillation of the simple pendulum depends on its length $(l)$, mass of the bob $(m)$ and acceleration due to gravity $(g)$. Derive the expression for its time period using method of dimensions.
Dimensions of stress are