The mass per unit length of a non-uniform rod OP of length $L$ varies as $m=k\frac{x}{L}$  where $k$ is a constant and $x$ is the distance of any point on the rod  from end O. the distance of the centre of mass of the rod from end O is $\frac{2L}{p}$  then $p$ is

Consider a rod OP of length L lying along the x-axis with O as the origin (Fig. 5.74).consider a small element AB of length $dx$  at a distance $x$ from O.

Mass of element  $AB(=dm)=mdx=\frac{k}{L}\left(xdx\right)$
The distance of the centre of mass from O is given by 
     $x_{CM}=\frac{{\displaystyle \int \left(dM\right)x}}{{\displaystyle \int \left(M\right)}}=\frac{\frac{k}{L}{\displaystyle \underset{0}{\overset{L}{\int }}{x}^2}dx}{\frac{k}{L}{\displaystyle \underset{0}{\overset{L}{\int }}{x}^{ }}dx}$
               $=\frac{{\left|\frac{x^3}{3}\right|}_0^L}{{\left|\frac{x^2}{2}\right|}_0^L}=\frac{L^3/3}{L^2/2}=\frac{2L}{3}$