Find the dimensional formula of $\frac{a}{b}$ in the equation $F=a \sqrt{x}+b t^2$,where $F$ is force,$x$ is distance,and $t$ is time.

$A$ and $B$ possess unequal dimensional formulas. Then,which of the following operations is not possible in any case?

If $A$ and $B$ are two physical quantities having different dimensions,then which of the following cannot denote a physical quantity?

The dimensional formula of $\frac{1}{\mu_{0} \varepsilon_{0}}$ is . . . . . . .

Heat produced in a current-carrying conducting wire depends on current $I$,resistance $R$ of the wire,and time $t$ for which the current is passed. Using these facts,obtain the formula for heat energy.

$A$ wave pulse can travel along a tense string like a violin string. $A$ series of experiments showed that the wave velocity $V$ of a pulse depends on the following quantities: the tension $T$ of the string,the cross-sectional area $A$ of the string,and the density $\rho$ (mass per unit volume) of the string. Obtain an expression for $V$ in terms of $T$,$A$,and $\rho$ using dimensional analysis.