Question

2 particles of masses 1g and 4g have equal momentum. what is the ratio between their kinetic energies?

Answer 1

let P1 be the momentum of 1st particle and P2 be the momentum of second particle..m1 be mass of 1st particle and m2 be the mass and 2nd particle.
v1 is the first particle velocity and v2 is the 2nd particle velocity

P1=P2
m1v1=m2v2
1*v1=4*V2
v1=4v2. => 1. equation

Let k1 for kinetic energy of 1st particle and k2 for 2nd for kinetic energy of 2nd particle.
k1=1*v1
k1=4v2. ( from 1st equation)........{2}

k2=4*v2. {3}
{2}/{3}

k1 = k2