Final answer:
The accelerations of two objects of different masses on a frictionless inclined ramp without air resistance are the same. This equality is because the acceleration depends only on gravity and the angle of the incline, not the mass of the objects.
Step-by-step explanation:
When two objects, one with mass m and the other with mass 5m, are placed on a frictionless inclined ramp with no air resistance, the force of gravity pulling each object down the slope is their weight component along the incline. According to Newton's second law (Fnet = ma), the net force acting on an object is equal to the mass of the object multiplied by its acceleration. Since both objects are subject to the same gravitational acceleration and the inclined angle is the same for both objects, the component of gravitational force along the slope for both objects will cause them to have the same acceleration.
In the absence of friction and air resistance, all objects slide down a frictionless incline with the same acceleration if the angle of the incline is identical. This is because the acceleration down the incline is given by the equation a = g sin(θ), which does not depend on the mass of the object, where g is the acceleration due to gravity and θ is the angle of the incline. Therefore, the truth is option 2: The acceleration of the object with mass m is equal to the acceleration of the object with mass 5m.