Question

A light body and a heavy body have same linear momentum. Which one has greater K.E.?

Answer 1

If light and heavy body have equal momentam then lighter body will have higher kinetic energy, since it's velocity have to make up for its lighter mass.

Let , mass of lighter body = m , and velocity = v

Mass of heavy body = M, and velocity = V

Now since momentam is equal so ,

MV = mv

=> v = MV/m ( since M>m , so v > V)

Now KE(L) of lighter body = 1/2 m v^2 = 1/2 m ( MV/m) ^2

KE(H) of heavy mass = 1/2 MV^2

So KE (L) > KE(H)