Question

A nucleus at rest splits into two nuclear parts having radii in ratio $1:2.$ Their velocities will be in the ratio

• A. $8:1$
• B. $4:1$
• C. $2:1$
• D. $1:1$

Answer 1

The correct option is A $8:1$

Volume X density (same for both the fragments as both get generetaed from the same nucleus) = Mass

So, Mass of the fragments are in ratio of their volumes

Volume $\propto$ r

So, we have, $\frac{V_1}{V_2}$ = $\frac{m_1}{m_2}$ = $\frac{{r_1}^3}{{r_2}^3}$

So, $\frac{m_1}{m_2}$ = $1^3:2^3=1:8$.

So, by conservation of momentum $m_1{v}_1=m_2{v}_2$. So, the velocities are in ratio, $8:1$.