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

If the present units of length,time,and mass $(m, s, kg)$ are changed to $100 \; m, 100 \; s, 0.1 \; kg$,then:

The time period of a body undergoing simple harmonic motion is given by $T=p^{a} D^{b} S^{c}$,where $p$ is the pressure,$D$ is density,and $S$ is surface tension. The values of $a, b,$ and $c$ respectively are

In a particular system of units,a physical quantity can be expressed in terms of the electric charge $e$,electron mass $m_e$,Planck's constant $h$,and Coulomb's constant $k = \frac{1}{4 \pi \epsilon_0}$,where $\epsilon_0$ is the permittivity of vacuum. In terms of these physical constants,the dimension of the magnetic field is $[B] = [e]^\alpha [m_e]^\beta [h]^\gamma [k]^\delta$. The value of $\alpha + \beta + \gamma + \delta$ is . . . . .

Force $F$ is given by the equation $F = \frac{X}{\text{Linear density}}$. Then the dimensions of $X$ are:

The equation of state of a real gas is given by $(P+\frac{a}{V^2})(V-b)=RT$,where $P, V$ and $T$ are pressure,volume and temperature respectively and $R$ is the universal gas constant. The dimensions of $\frac{a}{b^2}$ are similar to that of: