Two bodies with kinetic energies in the ratio | vedclass

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(D) The kinetic energy $E$ of a body with mass $m$ and linear momentum $p$ is given by the relation: $E = \frac{p^2}{2m}$.Since the linear momentum $p

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$1:4$

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(D) The kinetic energy $E$ of a body with mass $m$ and linear momentum $p$ is given by the relation: $E = \frac{p^2}{2m}$.Since the linear momentum $p$ is constant for both bodies,we have $E \propto \frac{1}{m}$,which implies $m \propto \frac{1}{E}$.Given the ratio of kinetic energies is $\frac{E_1}{E_2} = \frac{4}{1}$.Therefore,the ratio of their masses is $\frac{m_1}{m_2} = \frac{E_2}{E_1} = \frac{1}{4}$.Thus,the ratio of their masses is $1:4$.

Two bodies with kinetic energies in the ratio of $4 : 1$ are moving with equal linear momentum. The ratio of their masses is

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