Question

A light body and a heavy body have same momentum. Which one will have greater kinetic energy?

Answer 1

Mv=mV

let mass of heavy body=M

mass of light body=m

velocity of heavy body=v

velocity of light body=V

we know M>m.

then from Mv=mV

M/m=V/v

V>v

velocity of light body>velocity of heavy body

now kinetic energy is given by mv²/2

k.E for heavy body=Mv²/2=Mv.v/2 ...............(1)

k.E for light body=mV²/2=mV.V/2 ................(2)

from eqn (1) and (2) we can see that

we know

Mv=mV

so just have to compare

V/2 and v/2

we also know V>v

so V/2>v/2

from this we can conclude that

k.E for light body>k.E for heavy body