Final answer:
The ratio of linear momentum of body B to body A, given that both bodies have the same kinetic energy and mass ratio of 3:1, is 1:√3. This is because body B must have a higher velocity to have the same kinetic energy as the more massive body A.
Step-by-step explanation:
The student's question involves determining the ratio of linear momentum of two bodies with different masses but possessing the same kinetic energy. The linear momentum is a vector quantity that is the product of a system's mass and its velocity (option c). Using the given mass ratio of 3:1 and equal kinetic energies, we can say that body B must be moving faster than body A since it has less mass.
The kinetic energy (KE) for both bodies can be written as:
KE(A) = 0.5 * mass(A) * velocity(A)^2
KE(B) = 0.5 * mass(B) * velocity(B)^2
Because the kinetic energies are equal, we have:
mass(A) * velocity(A)^2 = mass(B) * velocity(B)^2
Substituting the mass ratio, we get:
(3 * mass(B)) * velocity(A)^2 = mass(B) * velocity(B)^2
This simplifies to:
velocity(B)^2 = 3 * velocity(A)^2
Thus:
velocity(B) = sqrt(3) * velocity(A)
To find the momentum ratio, we multiply mass by velocity for each body:
momentum(B) = mass(B) * velocity(B) = 1 * sqrt(3) * velocity(A)
momentum(A) = 3 * mass(B) * velocity(A)
The momentum ratio is then:
momentum(B) / momentum(A) = (sqrt(3) * velocity(A)) / (3 * velocity(A))
Which simplifies to:
momentum ratio = sqrt(3) / 3 = 1 / sqrt(3)
Therefore, the correct answer is (C) 1: √3.