The momentam of a light and heavy objects are same. Find the ratio of their kinetic energy. Whose kinetic energy is more?

Answer

`((E_(k))_(1))/((E_(k))_(2))=(m_(2))/(m_(1))`;
The kinetic energy of lighter object is more.

Explanation

Kinetic energy `E_(k)=(1)/(2)mv^(2)`
`=(1)/(2)mv^(2)xx(m)/(m)`
`=(1)/(2)(m^(2)v^(2))/(m)`
`=(p^(2))/(2m)(because p=mv)`
Here, the momentum of two objects is same.
So `E_(k)prop(1)/(m)`
`therefore` For lighter object `E_(k_(1))prop(1)/(m_(1))`
`therefore` For heavier object `E_(k_(2))prop(1)/(m_(2))`
`therefore (E_(k_(1)))/(E_(k_(2)))=(m_(2))/(m_(1))`
But, `m_(2)gtm_(1)`
`therefore (m_(2))/(m_(1))gt1`
``therefore (E_(k_(1)))/(E_(k_(2)))gt1`
`therefore E_(k_(1))gtE_(k_(2))`