A nucleus at rest disintegrates into two smal | vedclass

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(A) According to the law of conservation of linear momentum,since the initial nucleus is at rest,the initial momentum is $0$.Let the masses of the two

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In opposite directions with speeds in the ratio of $1:2$ respectively.

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(A) According to the law of conservation of linear momentum,since the initial nucleus is at rest,the initial momentum is $0$.Let the masses of the two nuclei be $m_1$ and $m_2$ and their velocities be $v_1$ and $v_2$ respectively.$p_i = p_f$$0 = m_1 v_1 + m_2 v_2$$m_1 v_1 = -m_2 v_2$Taking the magnitude of the velocities,we have $m_1 |v_1| = m_2 |v_2|$,which implies $\frac{|v_1|}{|v_2|} = \frac{m_2}{m_1}$.Given the ratio of masses is $\frac{m_1}{m_2} = \frac{2}{1}$,we substitute this into the ratio of speeds:$\frac{|v_1|}{|v_2|} = \frac{1}{2}$.The negative sign indicates that the nuclei move in opposite directions.Therefore,they move in opposite directions with speeds in the ratio of $1:2$.

$A$ nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of $2:1$. After disintegration,they will move:

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