Nucleus repeater into two nuclear part which have their velocity ratio

1.	Nucleus repeater into two nuclear part which have their velocity ratio equal to 3:2 determine the ratio of their nuclear size.
Answer» By conservation of linear momentum m₁v₁ = m₂v₂ \(\cfrac{m_1}{m_2}\) = \(\cfrac{v_2}{v_1}\) m = p.v \(\cfrac{p.v_1}{p.v_2}\) = \(\cfrac23\) \(\cfrac{\cfrac43\pi r_1^3}{\cfrac43\pi r_2^3}\) = \(\cfrac23\) \(\left(\cfrac{r_1}{r_2}\right)^3\) = \(\left(\cfrac23\right)\) \(\cfrac{r_1}{r_2}\) = \(\left(\cfrac23\right)^{1/3}\)

Nucleus repeater into two nuclear part which have their velocity ratio equal to 3:2 determine the ratio of their nuclear size.

Answer»

By conservation of linear momentum m₁v₁ = m₂v₂

\(\cfrac{m_1}{m_2}\) = \(\cfrac{v_2}{v_1}\)

m = p.v

\(\cfrac{p.v_1}{p.v_2}\) = \(\cfrac23\)

\(\cfrac{\cfrac43\pi r_1^3}{\cfrac43\pi r_2^3}\) = \(\cfrac23\)

\(\left(\cfrac{r_1}{r_2}\right)^3\) = \(\left(\cfrac23\right)\)

\(\cfrac{r_1}{r_2}\) = \(\left(\cfrac23\right)^{1/3}\)

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Nucleus repeater into two nuclear part which have their velocity ratio equal to 3:2 determine the ratio of their nuclear size.

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