Question

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

Answer 1

Let m and M be the masses of light and a heavy object moving with velocities v and V respectively.

As both have the same momentum,

∴ mv = MV

or `"M"/"V'` .........(i)

The kinetic energy of a light object,

`"K"_"m" = 1/2 "mv"^2`

The kinetic energy of a heavy object,

`"K"_"m' = 1/2 "mV"^2`

The kinetic energy of a heavy object,

`"K"_"M" = 1/2 "MV"^2`

∴ `("K"_"m")/("K"_"m") = (1/2 "mv"^2)/(1/2 "MV"^2)`

= `"m"/"M" xx ("M"/"m")^2`

= `"M"/"m"` (Using (i))

As M>m;

K_m > K_M, i.e. light object has larger kinetic energy.