Final answer:
The correct relationship between momentum p and kinetic energy k is that momentum is proportional to the square root of kinetic energy multiplied by mass, which is represented as p = m√k, making option 4 the correct choice.
Step-by-step explanation:
The correct relationship between momentum p and kinetic energy k of an object of mass m can be understood through the equations of motion and energy. The formula for kinetic energy is KE = 1/2mv², where m is the mass of the object and v is its velocity. The momentum of an object is given by p = mv. Since momentum p = mv and kinetic energy KE = 1/2mv², we can relate the two by expressing velocity in terms of momentum, v = p/m. Plugging that into the kinetic energy formula, we get KE = 1/2m(p/m)² = p²/(2m). Therefore, the relationship that momentum p is proportional to the square root of kinetic energy k multiplied by mass m is correct, which is represented by p = m√k, making option 4 the correct relationship.