If the formula, $X=3 Y Z^{2}, X$ and $Z$ have dimensions of capacitance and magnetic induction. The dimensions of $Y$ in $M K S Q$ system are

  • [AIIMS 2017]
  • A

    $\left[M^{-3} L^{-2} T^{4} Q^{4}\right]$

  • B

    $\left[M L^{2} T^{8} Q^{4}\right]$

  • C

    $\left[M^{-2} L^{-3} T^{2} Q^{4}\right]$

  • D

    $\left[M^{-2} L^{-2} T Q^{2}\right]$

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$A, B, C$ and $D$ are four different physical quantities having different dimensions. None of them is dimensionless. But we know that the equation $AD = C\, ln\, (BD)$ holds true. Then which of the combination is not a meaningful quantity ?

  • [JEE MAIN 2016]

A force is represented by $\mathrm{F}=a \mathrm{x}^2+\mathrm{bt}^{1 / 2}$. Where $\mathrm{x}=$ distance and $\mathrm{t}=$ time. The dimensions of $\mathrm{b}^2 / \mathrm{a}$ are :

  • [JEE MAIN 2024]

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According to Newton, the viscous force acting between liquid layers of area $A$ and velocity gradient $\Delta v/\Delta z$ is given by $F = - \eta A\frac{{\Delta v}}{{\Delta z}}$ where $\eta $ is constant called coefficient of viscosity. The dimension of $\eta $ are

  • [AIPMT 1990]

$M{L^{ - 1}}{T^{ - 2}}$ represents