If the momentum of a body is increased n time | vedclass

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(D) The relationship between kinetic energy $(E)$ and momentum $(P)$ for a body of mass $(m)$ is given by the formula:$E = \frac{P^2}{2m}$From this eq

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$n^2$ times

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(D) The relationship between kinetic energy $(E)$ and momentum $(P)$ for a body of mass $(m)$ is given by the formula:$E = \frac{P^2}{2m}$From this equation,we can see that kinetic energy is directly proportional to the square of the momentum:$E \propto P^2$If the momentum $(P)$ is increased $n$ times,the new momentum becomes $P' = nP$.Substituting this into the proportionality:$E' \propto (nP)^2 = n^2 P^2$Therefore,the new kinetic energy $(E')$ becomes $n^2$ times the original kinetic energy $(E)$.Thus,the kinetic energy increases by a factor of $n^2$.

If the momentum of a body is increased $n$ times,its kinetic energy increases by a factor of:

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