Two bodies of mass 4 ,g and 25 ,g are moving | vedclass

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(C) The kinetic energy $K$ of a body is related to its linear momentum $P$ and mass $m$ by the formula $K = \frac{P^2}{2m}$.Given that both bodies hav

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$2: 5$

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(C) The kinetic energy $K$ of a body is related to its linear momentum $P$ and mass $m$ by the formula $K = \frac{P^2}{2m}$.Given that both bodies have equal kinetic energies, we have $K_1 = K_2$.Therefore, $\frac{P_1^2}{2m_1} = \frac{P_2^2}{2m_2}$.Rearranging the terms to find the ratio of their momenta, we get $\frac{P_1^2}{P_2^2} = \frac{m_1}{m_2}$.Taking the square root on both sides, $\frac{P_1}{P_2} = \sqrt{\frac{m_1}{m_2}}$.Substituting the given masses $m_1 = 4 \,g$ and $m_2 = 25 \,g$, we get $\frac{P_1}{P_2} = \sqrt{\frac{4}{25}} = \frac{2}{5}$.Thus, the ratio of their linear momentum is $2: 5$.

Two bodies of mass $4 \,g$ and $25 \,g$ are moving with equal kinetic energies. The ratio of the magnitude of their linear momentum is:

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