Pressure exerted by a gas is found to be $50\, N/m^2$ , then the value of pressure in $CGS$ system is

A function $f(\theta )$ is defined as $f(\theta )\, = \,1\, - \theta  + \frac{{{\theta ^2}}}{{2!}} - \frac{{{\theta ^3}}}{{3!}} + \frac{{{\theta ^4}}}{{4!}} + ...$ Why is it necessary for  $f(\theta )$  to be a dimensionless quantity ?

A dimensionally consistent relation for the volume V of a liquid of coefficient of viscosity ' $\eta$ ' flowing per second, through a tube of radius $r$ and length / and having a pressure difference $P$ across its ends, is

In the relation $y = a\cos (\omega t - kx)$, the dimensional formula for $k$ is

In Vander Waals equation $\left[ P +\frac{ a }{ V ^{2}}\right][ V - b ]= RT$; $P$ is pressure, $V$ is volume, $R$ is universal gas constant and $T$ is temperature. The ratio of constants $\frac{a}{b}$ is dimensionally equal to .................