# Light and heavy objects have equal kinetic energy.which one has greater momentum?

Aug 8, 2018

Generally, for kinetic energy $T$ and momentum $p$:

$T = {p}^{2} / \left(2 m\right) \implies p = \sqrt{2 m T}$

For larger mass $M$ and smaller mass $m$:

 abs(p_("M"))/( abs(p_("m"))) = sqrt(cancel2 M cancelT)/sqrt(cancel2 m cancelT) = sqrt(M/m) qquad qquad gt 1 qquad because M gt m

So the larger mass has greater momentum

Thing to note is that momentum is a vector quantity so here we are looking at absolutes values of momentum. A mass with -ve velocity (and momentum) always has "smaller" momentum than any other mass with +ve velocity, simply due to the sign, but that might defeat the purpose of the question.