Question

A heavy nucleus at rest breaks into two fragments which fly off with velocities $8:1$. The ratio of radii of fragments is:-

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

Answer 1

The correct option is A $1:2$

Let mass and velocities of two fragments be $m_1,v_1,m_2,v_2$

As both fragments have the same density and volume of sphere $\propto r^3$

Applying conservation of momentum,

$m_1,v_1=m_2,v_2\Rightarrow v_1{r_1}^3=v_2{r_2}^3$
$\Rightarrow \frac{{r_1}^3}{{r_2}^3}=\frac{1}{8}$
$\Rightarrow \frac{r_1}{r_2}=\frac{1}{2}$