Question

a light and heavy object have the same momentum find out the ratio of their kinetic energies which one has a larger kinetic energies

Answer 1

Let the two bodies have masses m1 and m2 respectively such that m2 > m1 . Then, for first object p1 = m1v1 and for second object p2 = m2v2

But p1 = p2 or m1v1 = m2v2

Since m1 < m2, then v1 > v2

Now, K = 1/2 mv^2 = 1/2 pv, therefore,

K1/K2 = p1v1 / p2v2 = v1/v2

But v1 > v2

Therefore, kinetic energy of body of lesser mass is more.

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hope this helps .

Answer 2

Answer:

Let the mass of the lighter object be m₁ and of the heavier one be m₂, velocities be v₁ and v₂ and momentum be p.

Since their momentum is the same, p = m₁v₁ = m₂v₂.

Since, m₁ < m₂, v₁ > v₂.

Now, Kinetic Energy of object with mass m₁, EK₁ = (1/2)(m₁)(v₁)².

Kinetic energy of object with mass m₂, EK₂ = (1/2)(m₂)(v₂)².

EK₁ : EK₂ = (1/2)(m₁)(v₁)² ÷ (1/2)(m₂)(v₂)² = (m₁.v₁²)/(m₂.v₂²)

On comparing, EK₁ = m₁.v₁² and EK₂ = m₂.v₂²

Since, m₁ < m₂ and v₁ > v₂

EK₁ will be more than EK₂.

hope this will help u!!!!!

Explanation: