Final answer:
The correct answer to the question regarding the ratio of kinetic energies of two particles with equal linear momentum is C. m2/m1. This is because kinetic energy is directly proportional to the mass when linear momentum is held constant.
Step-by-step explanation:
In Physics, the mechanical energy of a system is the sum of its kinetic energy (KE) and potential energy (PE). It is governed by the Law of Conservation of Mechanical Energy, which states that in a closed system (a system where no external forces like friction or air resistance act), the total mechanical energy remains constant.
The formula for mechanical energy is given by KE + PE = constant.
Kinetic energy is the energy an object possesses due to its motion, and its formula is KE = ½mv², where 'm' is mass and 'v' is velocity.
Potential energy can take various forms, like gravitational potential energy, which depends on an object's position relative to Earth or another gravitational field.
When comparing two objects with equal linear momenta (p), recall that momentum (p) is given by the product of mass and velocity (p = mv).
However, since the two objects have equal momenta and we are looking for the ratio of their kinetic energies, we get KE1/KE2 = (½m1v1²)/(½m2v2²)
= (m1v1²)/(m2v2²).
Given that m1v1 = m2v2, we can conclude that v1²/v2² = m2/m1.
Substituting this into our kinetic energy ratio gives us KE1/KE2 = m2/m1.
Therefore, the correct answer to the question about the ratio of their kinetic energies is C. m2/m1.