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

A1 : 4

B4 : 1

C2 : 1

D1 : 2

Answer:

D. 1 : 2

Read Explanation:

  • 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



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