The formula is $X = 5YZ^2$,where $X$ and $Z$ have dimensions of capacitance and magnetic field,respectively. What are the dimensions of $Y$ in $SI$ units?

The amount of heat energy $Q$ used to heat up a substance depends on its mass $m$,its specific heat capacity $s$,and the change in temperature $\Delta T$ of the substance. Using the dimensional method,find the expression for $s$. (Given that $[s] = [L^2 T^{-2} K^{-1}]$)

Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimension of $L$,which of the following statement$(s)$ is/are correct?
$(1)$ The dimension of force is $L^{-3}$
$(2)$ The dimension of energy is $L^{-2}$
$(3)$ The dimension of power is $L^{-5}$
$(4)$ The dimension of linear momentum is $L^{-1}$

If the relationship between velocity,acceleration,and force in two systems is given by $v_2 = \frac{\alpha^2}{\beta} v_1$,$a_2 = \alpha \beta a_1$,and $F_2 = \frac{F_1}{\alpha \beta}$,then what is the relationship between mass,length,and time?

In electromagnetic theory, electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related. In the questions below, $[E]$ and $[B]$ stand for dimensions of electric and magnetic fields respectively, while $[\varepsilon_0]$ and $[\mu_0]$ stand for dimensions of the permittivity and permeability of free space respectively. $[L]$ and $[T]$ are dimensions of length and time respectively. All quantities are in $SI$ units.
$(1)$ The relation between $[E]$ and $[B]$ is:
$(A)$ $[E] = [B][L][T]$
$(B)$ $[E] = [B][L]^{-1}[T]$
$(C)$ $[E] = [B][L][T]^{-1}$
$(D)$ $[E] = [B][L]^{-1}[T]^{-1}$
$(2)$ The relation between $[\varepsilon_0]$ and $[\mu_0]$ is:
$(A)$ $[\mu_0] = [\varepsilon_0][L]^2[T]^{-2}$
$(B)$ $[\mu_0] = [\varepsilon_0][L]^{-2}[T]^2$
$(C)$ $[\mu_0] = [\varepsilon_0]^{-1}[L]^2[T]^{-2}$
$(D)$ $[\mu_0] = [\varepsilon_0]^{-1}[L]^{-2}[T]^2$
Give the answers for questions $(1)$ and $(2)$.

If $z = xP + G$,where $P$ is pressure and $G$ is the universal gravitational constant; then the dimensional formulas for $x$ and $z$ respectively are (here,$G = \frac{Fr^2}{m_1 m_2}$,$P = \frac{\text{Thrust}}{\text{Area}}$).