Question

A nucleus disintegrates into two nuclear parts which have their velocities in the ratio 2 : 1. The ratio of their nuclear sizes will be:

• A. $2^{1/3}:1$
• B. $1:3^{1/2}$
• C. $3:1$
• D. $1:2^{1/3}$

Answer 1

The correct option is D $1:2^{1/3}$

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:

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