Embibe Experts Solutions for Chapter: Physical World and Measurement, Exercise 4: Exercise-4

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

If $V$ , denotes the potential difference across the plates of a capacitor of capacitance $C,$ the dimensions of $C{V}^2$ are

In the relation ; $P=\frac{\alpha }{\beta }{e}^{-\frac{\alpha Z}{k\theta }}$, $P$ is pressure, $Z$ is distance, $k$ is Boltzman constant and $\theta$ is the temperature. The dimensions of $\beta$ will be:

The equation $\left(p+\frac{a}{V^2}\right) \left(V-b\right)$= constant. The units of $a$ are:

If the dimensions of length are expressed as $G^x{c}^y{h}^z;$ where $G, c$ and $h$ are the universal gravitational constant, speed of light and Planck's constant respectively, then

The velocity $v$ of a particle at time t is given by $v=\mathrm{a}\mathrm{t}+\frac{b}{t+c}$, where $a, b$ and $c$ are constant. The dimensions of $a, b$ and $c$ are respectively:

The $\mathrm{SI}$ unit of universal gas constant $\left(\mathrm{R}\right)$ is

A sheet of area $40{ \mathrm{m}}^2$ is used to make an open tank with a square base, then find the dimensions of the base such that volume of this tank is maximum.