In a particular fission process of a uranium atom at rest, fragments with mass numbers $A_{1}$ and $A_{2}$ are produced. A good estimate of the ratio of kinetic energies of the fragments, $K_{1} / K_{2}$ is :

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$A_{1} / A_{2}$

${(A_{2} / A_{1})}^{2}$

${(A_{1} / A_{2})}^{2}$

$A_{2} / A_{1}$

answer is A.

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Detailed Solution

By COM we can say that both the fragments have same linear momentum

we have $k = \frac{P^{2}}{2 m}$

$k \propto \frac{1}{m}$ when $P$ is same

$\frac{k_{1}}{k_{2}} = \frac{m_{2}}{m_{1}} = \frac{A_{2}}{A_{1}}$

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