A block of mass $m$ is placed on a surface with a vertical cross section given by $y=\large\frac{x^3}{6}$. If the coefficient of friction is $0.5$, the maximum height above the ground at which the block can be placed without slipping is :

Question

$\begin{array}{1 1}(A)\;\frac{1}{3}\;m\\ (B)\;\frac{1}{2}\;m \\(C)\;\frac{1}{6}\;m \\(D)\;\frac{2}{3}\;m \end{array} $