Question

Two masses M1 = M and M2 = 4M possess an equal amount of kinetic energy, then the ratio of their momentum p1 : p2 is?

• A. 1 : 4
• B. 4 : 1
• C. 2 : 1
• D. 1 : 2

Answer 1

Answer:

D. 1 : 2

• Kinetic Energy = 1/2 mv²

• Linear momentum, P = mv

• Relation between Linear momentum and KE is

Kinetic Energy = 1/2 mv²= P²/2m

Given in the question, KE is equal for both objects, that is,

P₁²/2M₁ = P₂²/2M₂

Given in the question,

• M₁ = M

• M₂ = 4M

Then the ratio of their momentum P₁ : P₂ is,

P₁²/2M₁ = P₂²/2M₂

P₁ ² / P₂²= 2M₁ / 2M₂

P₁ / P₂= √2M₁ / √2M₂

P₁ / P₂= √2M/ √2 x 4M

P₁ / P₂= √2/√8 = 1/√4 = 1/2

P₁ : P₂ = 1:2