Question

find the ratio of linear momentum of two particles of masses 1 kg and 4 Kg if the Kinetic energies are equal

Answer 1

here we know that k= p²/2m
so if k is constant than p is directly proportional to √m

so P1/P2 = √m1/√m2
= 1/2

Answer 2

K = 0.5 mv^2
p = mv

From above two equations, the relation between K and p is
. p = sqrt(2mK)

For two objects of same Kinetic energy (K)

p ∝ sqrt(m)

p1 : p2 = sqrt(m1) : sqrt(m2) = sqrt(1 kg) : sqrt(4 kg) = 1 : 2

Ratio of their linear momentum is 1 : 2