A light and a heavy object have the same momentum. Find out the ratio of their kinetic energies. Which one has a larger kinetic energy ?

Explanation

Suppose `m_(1)` and `m_(2)` are masses of a light and a heavy objects, respectively. As we know
`"kinetic energy"(K)=(1)/(2)mv^(2)" "[v="velocity of objects"].....(i)`
and movementum (p) = mv …..(ii)
Multiplying and dividing with m in Eqs. (i)
So, `K=(1)/(2)(mv^(2)xxm)/(m)rArr(1)/(2)(mv)^(2)/(m)"as from Eqs.(ii)"" "(p=mv)`
So, `K(P^(2))/(2m)` we have, kinetic energy, `K(P^(2))/(2m)`
`:'"Momentum is same for light and heavy body"`
So, kinetic energy, `Kprop(1)/(m)`
Thus, kinetic energy is inversely proprotional to the mass.
So, lighter body has larger kinetic energy.