A small object of uniform density rolls up a curved surface with an initial velocity '$\upsilon$'. It reaches upto a maximum height of $\frac{3{\upsilon }^2}{4g}$with respect to the initial position. The object is

When the body rolls up along the inclined plane, at the highest point, all its rotational KE will be converted to gravitational PE. Hence, height attained, $\mathrm{h}=\frac{3{\mathrm{v}}^2}{4\mathrm{g}}$ where $\nu$ is the velocity of centre of mass of the rolling body. Applying law of coservation of energy, total KE = mgh

$\frac{1}{2}{\mathrm{mv}}^2(1+\frac{{\mathrm{K}}^2}{{\mathrm{R}}^2})=\mathrm{mgh}\Rightarrow 1+\frac{{\mathrm{K}}^2}{{\mathrm{R}}^2}=2\mathrm{gh}=2\mathrm{g}\frac{3{\mathrm{v}}^2}{4\mathrm{g}}$

$\frac{{\mathrm{K}}^2}{{\mathrm{R}}^2}=\frac{1}{2}$

It could be a disc or solid cylinder