Question

$n=-D\left[\frac{\left(n_{2}-n_{1}\right)}{\left(x_{2}-x_{1}\right)}\right]$ , where $n$ is number of particles in unit area perpendicular to $x$-axis in unit time, $n_1$, $n_2$ are number of particles per unit volume, $x_2$ and $x_1$ are distance of two points from any point, then the dimension of $D$ is

• A. $[L^2T^{-1}]$
• B. $[L^{-2}T^{-1}]$
• C. $[L^{-2}T^{1}]$
• D. $[L^3T^{-1}]$

Answer 1

Answer: (B)

$[L^{-2}T^{-1}]$

Answer 2

$\left[n\right]=\frac{1}{\left[Area\,\times\,Time\right]}=\frac{1}{\left[L^{2}T\right]}$ $=\left[L^{-2}T^{-1}\right]$ $\left[x_{2}\right]=\left[x_{1}\right]=\left[L\right]$ and $\left[n_{2}-n_{1}\right]=\frac{1}{Volume}=\frac{1}{\left[L^{3}\right]}=\left[L^{-3}\right];$ $\Rightarrow \left[D\right]=\left[\frac{L^{-2}T^{-1}\,\times\,L}{L^{-3}}\right]$ $=\left[L^{2}T^{-1}\right]$