Question

two bodies of masses 3kg and 7kg respectively are moving at same velocity .The ratio of their kinetic energy is ?

Answer 1

Explanation:

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.

Answer 2

Explanation:

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