Final answer:
The mass of m on a frictionless inclined plane is determined by using Newton's second law and equating the gravitational force component with the tension for a system in static equilibrium.
Step-by-step explanation:
The mass of m on a frictionless inclined plane can be determined through the application of Newton's second law, using the components of gravitational force parallel and perpendicular to the plane. Since the problem statement indicates that the system is in static equilibrium, we are interested in the conditions under which the forces are balanced. For a mass on an inclined plane at an angle θ, the component of the gravitational force acting down the slope is mg sin θ, and this is balanced by the tension in the string. When this tension is also responsible for holding up another mass m, the two forces must be identical for equilibrium: mg sin θ = mg. This simplifies to m=M sin θ, which yields the mass m directly. This calculation assumes the mass of the pulley and string are negligible and there is no friction. When the problem includes a pulley with a mass or radius, or frictional forces, the calculation would need to take these into account, using the force balance and torque balance equations respectively.