When the sphere reaches its lowest position it loses gravitational potential energy by $∆$U and gains a kinetic energy by $∆$K, where $∆$U = -mg(R - r)

$\begin{array}{l}\text{ and }\mathrm{\Delta }K=\frac{1}{2}m{v}_c^2\left(1+\frac{K^2}{R^2}\right)=\frac{1}{2}m{v}^2\left(1+\frac{2}{5}\right)=\frac{7}{10}m{v}^2\\ \text{ According to conservation of energy, }\mathrm{\Delta }U+\mathrm{\Delta }K=0\\ \text{ or }-mg(R-r)+\frac{7}{10}m{v}^2=0\\ \text{ or }v=\sqrt{\frac{10}{7}g(R-r)}\end{array}$