b
\(\frac{ v _1}{ v _2}=\frac{3}{2}\)

\(m _1 v _1= m _2 v _2 \Rightarrow \frac{ m _1}{ m _2}=\frac{2}{3}\)

Since, Nuclear mass density is constant

\(\frac{ m _1}{\frac{4}{3} \pi r _1^3}=\frac{ m _2}{\frac{4}{3} \pi r _2^3}\)

\(\left(\frac{ r _1}{ r _2}\right)^3=\frac{ m _1}{ m _2}\)

\(\frac{ r _1}{ r _2}=\left(\frac{2}{3}\right)^{\frac{1}{3}}\)

\(\text { So, } x =2\)