The centre of mass of a disc of radius $\frac{8}{\sqrt{5}} \mathrm{m}$ is moving with a velocity of $4 \mathrm{m} {\mathrm{s}}^{-1}$ on a horizontal plane. The angular velocity of the disc about its centre is $\sqrt{5} \mathrm{rad} {\mathrm{s}}^{-1}$. Find the radius of curvature of the point $P$ shown in the figure (in meter).