Final answer:
The correct answer to the question about the ratio of linear momenta of two bodies with equal kinetic energies but different masses is option C, which represents the ratio as the square root of mass one to the square root of mass two.
Step-by-step explanation:
The question is asking about the relationship between the kinetic energies and linear momenta of two bodies with masses m1 and m2. Given that the kinetic energies of the two bodies are equal, we can express that as KE1 = KE2, which translates to (1/2)m1v12 = (1/2)m2v22 after applying the equation for kinetic energy (KE = (1/2)mv2).
To find the ratio of their momenta (p1 = m1v1 and p2 = m2v2), we can rearrange the previous equation to find the velocities (v1 and v2) in terms of masses and equate the two expressions for kinetic energy, which will ultimately reveal the relationship between the linear momenta. Upon doing so, we'll discover that the linear momenta are related by the ratio of the square roots of the masses: p1 : p2 = √m1 : √m2, therefore the correct answer is option C. √m1 : √m2.