Question

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

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

Answer 1

The correct option is A $1:2$

Given momentum conservation

$m_1{v}_1=m_2{v}_2$

$\frac{v_1}{v_2}=\frac{8}{1}=\frac{m_2}{m_1}$

So,

$\frac{m_1}{m_2}=\frac{1}{8}$

We know that

$m=\frac{v}{d}$

Here,

m=mass

v=volume

d=density

But when particle breaks then density become constant

So,

$v\propto m$

$\frac{v_1}{v_2}=\frac{m_1}{m_2}$

$\frac{a_1^3}{a_2^3}=\frac{1}{8}$

$\frac{a_1}{a_2}={\left(\frac{1}{8}\right)}^{\frac{1}{3}}$

$\frac{a_1}{a_2}=\frac{1}{2}$