If $E$ and $E_0$ represent the energies, and $t$ and $t_0$ represent the times, which of the following relations is dimensionally correct?

Given the pressure formula $P = FK$,where $F$ is force,find the dimensional formula of $K$.

Using dimensional analysis,the resistivity in terms of fundamental constants $h, m_{e}, c, e, \varepsilon_{0}$ can be expressed as

The Young's modulus of a wire is given by $Y = \frac{F}{A} \cdot \frac{L}{\Delta L}$,where $L$ is length,$A$ is cross-sectional area,and $\Delta L$ is the change in length. By what factor must we multiply to convert the value from $CGS$ units to $MKS$ units?

Consider an expression $Q V = k P T L^\alpha$ where $V, P, T, L$ are volume, pressure, time, and length respectively. The quantity $[Q]$ has dimension $M L^{-1} T^{-1}$. $k$ is a dimensionless constant. The value of the integer $\alpha$ is:

$A$ charged particle of charge $e$ and mass $m$ is moving in an electric field $\vec{E}$ and magnetic field $\vec{B}$. Construct dimensionless quantities and quantities of dimension $T^{-1}$.