Question

a light object and heavy object have same momentum. find out the ratio of their kinetic energies.

Answer 1

the 2 objects have same momentum and the heavier object has more mass .....so the lighter object must have greater kinetic energy in order to create same momenta ( as compared to the heavier object ) now kinetic energy depends on mass and velocity's square so clearly K.E of lighter object is greater than the K.E of the heavier object .
now,
ratio of their K.E ,
K.E of heavier of object = 1/2Mv²
K.E. of lighter object = 1/2mv²
therefore their ration = 1/2Mv²/1/2mv² = m/M

i hope it helps.....................