A solid sphere is rolling on a frictionless surface, shown in...

From conservation of energy Potential energy = translational kinetic energy + rotational kinetic energy \begin{array}{r} m g h=\frac{1}{2} m v^2+\frac{1}{2}\left(\frac{2}{5}\right) m R^2 \cdot \frac{v^2}{R^2} \\ \Rightarrow \quad \frac{7}{10} m v^2=m g h \Rightarrow v \geq \sqrt{\frac{10}{7} g h} \end{array}