Question

A nucleus ruptures into two parts have their velocity ratio 2 : 1. The ratio of nuclear radius of two parts respectively is

Answer 1

$\Large\underline{\underline{\sf Given:}}$

• A nucleus ruptures into two parts have their velocity ratio $\sf{(v_1:v_2)}$=2 : 1

$\Large\underline{\underline{\sf To\:Find:}}$

• The ratio of nuclear radius of two parts.

$\Large\underline{\underline{\sf Solution:}}$

By Conservation of Momentum

$\implies{\sf m_1u_1+m_2u_2=m_1v_1+m_2v_2 }$

$\implies{\sf 0=m_1v_1+m_2v_2}$

$\implies{\sf -m_2v_2=m_1v_1}$

$\implies{\sf \dfrac{-m_2}{m_1}=\dfrac{v_1}{v_2} }$

$\implies{\sf -\dfrac{m_2}{m_1}=\dfrac{2}{1}}$

$\implies{\sf -\dfrac{m_2}{m_1}=2}$

Negative sign indicates velocity is in opposite direction.

$\implies{\sf \dfrac{m_2}{m_1}=\dfrac{2}{1}}$

$\large{\boxed{\sf m=\dfrac{4}{3}πr^3×\rho }}$

$\implies{\sf \dfrac{m_2}{m_1}=\left(\dfrac{r_2}{r_1}\right)^3 }$

$\implies{\sf \dfrac{r_1}{r_2}=\dfrac{1}{(2)^{1/3})} }$

$\Large\underline{\underline{\sf Answer:}}$

•°• Ratio of nuclear radius of two parts respectively is $\sf{(r_1:r_2)}$=$\sf{1:(2)^{1/3}}$ .