Question

2 particles of mass 1kg and 5 kg have same momentum calculate ratio of their kinetic energy?

Answer 1

Let mass of first body = m₁ = 3 kg

Let mass of second body = m₂ = 5 kg

So, m₁ / m₂ = 3 / 5

Also suppose that v₁ and v₂ be the velocities of the first and second body respectively.

We have to find the ratio of their kinetic energies i-e, K₁ : K₂

K₁ and K₂ are the kinetic energy of bodies.

Since,

K₁ = 1/2 m₁v₁²   ............ (1)

K₂ = 1/2 m₂v₂²   ............ (2)

Also, momentum of two bodies is given as :

P₁ = m₁v₁

P₂ = m₂v₂

Given that the bodies have same momentum.

Therefore,

P₁ = P₂

m₁v₁ = m₂v₂

m₁ / m₂ = v₂ / v₁

3 / 5 = v₂ / v₁   ........... (3)

Now, we find the ratio of both kinetic energies.

K₁ / K₂ = 1/2 m₁v₁² / 1/2 m₂v₂²

K₁ / K₂ = ( m₁/m₂ ).(v₁²/v₂²)

K₁ / K₂ = (3/5).(5/3)²     (Using equation (3))

K₁ / K₂ = (3/5).(25/9)

K₁ / K₂ = 5 / 3

which shows that,

K₁ : K₂ = 5 : 3

It is the required ratio of kinetic energies of both bodies.

It clearly shows that first body has more kinetic energy as compared to the second body.

Hope it helps you. Thanks.

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