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

The equation of state of some gases can be expressed as $\left( {P + \frac{a}{{{V^2}}}} \right)\,(V - b) = RT$. Here $P$ is the pressure, $V$ is the volume, $T$ is the absolute temperature and $a,\,b,\,R$ are constants. The dimensions of $'a'$ are

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. 

Which of the following is dimensionally correct

If time $(t)$, velocity $(u)$, and angular momentum $(I)$ are taken as the fundamental units. Then the dimension of mass $({m})$ in terms of ${t}, {u}$ and ${I}$ is

A physical quantity $\vec{S}$ is defined as $\vec{S}=(\vec{E} \times \vec{B}) / \mu_0$, where $\vec{E}$ is electric field, $\vec{B}$ is magnetic field and $\mu_0$ is the permeability of free space. The dimensions of $\vec{S}$ are the same as the dimensions of which of the following quantity (ies)?

$(A)$ $\frac{\text { Energy }}{\text { charge } \times \text { current }}$

$(B)$ $\frac{\text { Force }}{\text { Length } \times \text { Time }}$

$(C)$ $\frac{\text { Energy }}{\text { Volume }}$

$(D)$ $\frac{\text { Power }}{\text { Area }}$