The displacement $y$ of a particle at a distance $x$ at time $t$ for a transverse wave is given by $y = a \sin(bt - cx)$,where $a, b,$ and $c$ are constants. The dimensions of $b/c$ are the same as those of:

Given the pressure formula $P = FK$,where $F$ is force,find the dimensional formula of $K$.

The number of particles crossing a unit area perpendicular to the $X$-axis in unit time is given by $n = -D \frac{n_2 - n_1}{x_2 - x_1}$,where $n_1$ and $n_2$ are the number of particles per unit volume at positions $x_1$ and $x_2$ respectively. Find the dimensions of $D$,which is known as the diffusion constant.

The dimensions of the product $\mu_{0} \varepsilon_{0}$ are related to those of velocity as

If force $(F)$,length $(L)$,and time $(T)$ are assumed to be fundamental units,then the dimensional formula of mass will be:

Applying the principle of homogeneity of dimensions,determine which one is correct. Where $T$ is time period,$G$ is gravitational constant,$M$ is mass,and $r$ is the radius of the orbit.