\(\frac{1}{2} mv ^{2}= h v-\phi\)

\(v =\sqrt{\frac{2( hv -\phi)}{ m }}\)

\(\quad\) Given \(hv _{1}=2 \phi\)

\(hv _{2}=10 \phi\)

\(\therefore \frac{ v _{1}}{ v _{2}}=\sqrt{\frac{ hv _{1}-\phi}{ hv _{2}-\phi}}\)

\(\frac{ v _{1}}{ v _{2}}=\sqrt{\frac{2 \phi-\phi}{10 \phi-\phi}}=\frac{1}{3}\)