a
According to the Einstein's photoelectric equation, \(E=W_{0}+\frac{1}{2} m v^{2}\)

When frequency of incident light is \(2 v_{0}\)

\(h\left(2 v_{0}\right)=h v_{0}+\frac{1}{2} m v_{1}^{2} \Rightarrow h v_{0}=\frac{1}{2} m v_{1}^{2}\)    ..... \((i)\)

When frequency of incident light is \(5 v_{0}\)

\(h\left(5 v_{0}\right)=h v_{0}+\frac{1}{2} m v_{2}^{2} \Rightarrow 4 h v_{0}=\frac{1}{2} m v_{2}^{2}\)    ..... \((ii)\)

Dividing (i) by (ii), \(\frac{1}{4}=\frac{v_{1}^{2}}{v_{2}^{2}}\) or \(\frac{v_{1}}{v_{2}}=\frac{1}{2}\)