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

  • [JEE MAIN 2023]
  • A

    $Nm ^3\,C ^{-1} ; Nm ^2 \,C ^{-1}$

  • B

    $Nm ^2\, C ^{-1} ; Nm ^3 \,C ^{-1}$

  • C

    $Nm ^3 \,C ; Nm ^2 \,C$

  • D

    $Nm ^2 \,C ; Nm ^3\, C$

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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

  • [JEE MAIN 2024]

Let us consider an equation

$\frac{1}{2} m v^{2}=m g h$

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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.

  • [JEE MAIN 2021]