Two particles have masses in the ratio 1 : 2. | vedclass

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(C) The relationship between kinetic energy $(K)$, momentum $(p)$, and mass $(m)$ is given by the formula $K = \frac{p^2}{2m}$.From this, we can expre

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$1 : \sqrt{2}$

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(C) The relationship between kinetic energy $(K)$, momentum $(p)$, and mass $(m)$ is given by the formula $K = \frac{p^2}{2m}$.From this, we can express momentum as $p = \sqrt{2mK}$.Given that the kinetic energies are the same $(K_1 = K_2 = K)$, the ratio of the momenta of the two particles is:$\frac{p_1}{p_2} = \frac{\sqrt{2m_1K}}{\sqrt{2m_2K}} = \sqrt{\frac{m_1}{m_2}}$.Given the ratio of masses is $\frac{m_1}{m_2} = \frac{1}{2}$, we substitute this into the equation:$\frac{p_1}{p_2} = \sqrt{\frac{1}{2}} = \frac{1}{\sqrt{2}}$.Therefore, the ratio of their momenta is $1 : \sqrt{2}$.

Two particles have masses in the ratio $1 : 2$. If they have the same kinetic energy, what is the ratio of their momenta?

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