Write the dimensions of $a / b$ in the relation $P = \frac{a - t^2}{bx}$; where $P$ is the pressure,$x$ is the distance,and $t$ is the time.

Force $F$ is given in terms of time $t$ and distance $x$ by $F = a \sin(ct) + b \cos(dx)$. Then the dimension of $a/b$ is:

Stokes' law states that the viscous drag force $F$ experienced by a sphere of radius $a$,moving with a speed $v$ through a fluid with coefficient of viscosity $\eta$,is given by $F=6 \pi \eta a v$. If this fluid is flowing through a cylindrical pipe of radius $r$,length $l$ and pressure difference of $p$ across its two ends,then the volume of water $V$ which flows through the pipe in time $t$ can be written as $\frac{V}{t}=k\left(\frac{p}{l}\right)^a \eta^b r^c$,where $k$ is a dimensionless constant. Correct values of $a, b$ and $c$ are

$A$ neutron star with magnetic moment of magnitude $m$ is spinning with angular velocity $\omega$ about its magnetic axis. The electromagnetic power $P$ radiated by it is given by $\mu_{0}^{x} m^{y} \omega^{z} c^{u}$,where $\mu_{0}$ and $c$ are the permeability and speed of light in free space,respectively. Then,

The Young's modulus of a wire is given by $Y = \frac{F}{A} \cdot \frac{L}{\Delta L}$,where $L$ is length,$A$ is cross-sectional area,and $\Delta L$ is the change in length. By what factor must we multiply to convert the value from $CGS$ units to $MKS$ units?

The equation of state of some gases can be expressed as $(P + \frac{a}{V^2}) = \frac{b\theta}{l}$,where $P$ is the pressure,$V$ is the volume,$\theta$ is the absolute temperature,and $a$ and $b$ are constants. The dimensional formula of $a$ is