Question

Two particles having mass ratio 4:5 have same kinetic energy calculate ratio of linear momentum

Answer 1

Given ratio of masses 1 and 2  m₁ : m₂ = 4:5

also mentioned that kinetic energy of 1 and 2 are equal.

Thus K.E₁ = K.E₂ -----(A)

But Kinetic energy K.E =  1/2 mv² -----(B)

Hence reducing B in A we get,

(1/2) m₁ v₁² =(1/2) m₂ v₂² -----(C)

m₁/m₂ = v₂²/v₁²

4/5 = v₂²/v₁²

v₂ : v₁ = 2:√5 -----(D)

Also we know momentum p = m v

Now we can write the equation (C) as

(m₁ v₁)v₁ = (m₂ v₂)v₂

p₁v₁ = p₂v₂

p₁/p₂ =  v₂/v₁

p₁ : p₂ = 2:√5 (from D)