If speed $V$,area $A$,and force $F$ are chosen as fundamental units,then the dimension of Young's modulus will be:

In terms of potential difference $V$,electric current $I$,permittivity $\varepsilon_0$,permeability $\mu_0$,and speed of light $c$,the dimensionally correct equation$(s)$ is(are):
$(A)$ $\mu_0 I^2 = \varepsilon_0 V^2$
$(B)$ $\varepsilon_0 I = \mu_0 V$
$(C)$ $I = \varepsilon_0 cV$
$(D)$ $\mu_0 cI = V$

The work done by a gas molecule in an isolated system is given by $W = \alpha \beta^{2} e^{-\frac{x^{2}}{\alpha kT}}$,where $x$ is the displacement,$k$ is the Boltzmann constant,$T$ is the temperature,and $\alpha$ and $\beta$ are constants. Then the dimension of $\beta$ will be:

$A$ physical quantity $P$ is given by $P = \epsilon_0 L \frac{\Delta V}{\Delta t}$,where $\epsilon_0$ is electric permittivity,$L$ is length,$\Delta V$ is potential difference,and $\Delta t$ is time interval. The dimensional formula of $P$ is the same as that of

In a nuclear power plant,the energy released depends on the mass of the uranium sample $(m)$,the length of the oscillator $(\ell)$,and the frequency $(f)$ of oscillation as $E = m^{x} \ell^{y} f^{z}$. Then,what is the value of $x + y + z$?

The equation of a circle is given by $x^2+y^2=a^2$,where $a$ is the radius. If the equation is modified to change the origin to a point other than $(0,0)$,find the correct dimensions of $A$ and $B$ in the new equation: $(x-At)^2+(y-\frac{t}{B})^2=a^2$. The dimensions of $t$ are given as $[T^{-1}]$.