Question

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

Answer 1

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

`T = p^2/(2m) 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.