Question:
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
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