Electric field in a certain region is given by $\overrightarrow{ E }=\left(\frac{ A }{ x ^2} \hat{ i }+\frac{ B }{ y ^3} \hat{ j }\right)$. The $SI$ unit of $A$ and $B$ are
$Nm ^3\,C ^{-1} ; Nm ^2 \,C ^{-1}$
$Nm ^2\, C ^{-1} ; Nm ^3 \,C ^{-1}$
$Nm ^3 \,C ; Nm ^2 \,C$
$Nm ^2 \,C ; Nm ^3\, C$
Consider two physical quantities A and B related to each other as $E=\frac{B-x^2}{A t}$ where $E, x$ and $t$ have dimensions of energy, length and time respectively. The dimension of $A B$ is
Let us consider an equation
$\frac{1}{2} m v^{2}=m g h$
where $m$ is the mass of the body. velocity, $g$ is the acceleration do gravity and $h$ is the height. whether this equation is dimensionally correct.
If force $F$ , velocity $V$ and time $T$ are taken as fundamental units then dimension of force in the pressure is
In a new system of units energy $(E)$, density $(d)$ and power $(P)$ are taken as fundamental units, then the dimensional formula of universal gravitational constant $G$ will be .......
Which of the following equations is dimensionally incorrect?
Where $t=$ time, $h=$ height, $s=$ surface tension, $\theta=$ angle, $\rho=$ density, $a, r=$ radius, $g=$ acceleration due to gravity, ${v}=$ volume, ${p}=$ pressure, ${W}=$ work done, $\Gamma=$ torque, $\varepsilon=$ permittivity, ${E}=$ electric field, ${J}=$ current density, ${L}=$ length.