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Question

(A) The relationship between kinetic energy $(K)$ and linear momentum $(p)$ is given by $K = \frac{p^2}{2m}$, which implies $p = \sqrt{2mK}$.Given mas

Vedclass · Accepted Answer

$\frac{1}{\sqrt{2}}$

Vedclass · Answer

(A) The relationship between kinetic energy $(K)$ and linear momentum $(p)$ is given by $K = \frac{p^2}{2m}$, which implies $p = \sqrt{2mK}$.Given masses are $m_1 = m$ and $m_2 = 4m$.Given kinetic energies are $K_1$ and $K_2$ such that $\frac{K_1}{K_2} = \frac{2}{1}$.The ratio of their linear momenta is $\frac{p_1}{p_2} = \sqrt{\frac{2m_1 K_1}{2m_2 K_2}} = \sqrt{\frac{m_1}{m_2} 	imes \frac{K_1}{K_2}}$.Substituting the values: $\frac{p_1}{p_2} = \sqrt{\frac{m}{4m} 	imes \frac{2}{1}} = \sqrt{\frac{1}{4} 	imes 2} = \sqrt{\frac{1}{2}} = \frac{1}{\sqrt{2}}$.Thus, the ratio of their linear momenta is $\frac{1}{\sqrt{2}}$.

Two particles have masses $m$ and $4m$, and their kinetic energies are in the ratio $2:1$. What is the ratio of their linear momenta?

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