Question

2 bodies of masses 3kg and 5kg have the same momentum . Find out the ratios of their kinetic energies . Which one has a larger kinetic energy.

Answer 1

the answer the question is in the figure.

Answer 2

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.