Option 1 states that all periodic motions are necessarily simple harmonic. This statement is incorrect. While all simple harmonic motions are periodic, the reverse is not true. There are periodic motions that are not simple harmonic, such as the motion of a pendulum with small amplitudes.

Option 2 correctly states that all simple harmonic motions are necessarily periodic. Simple harmonic motion refers to the motion of an object that oscillates back and forth around an equilibrium position with a force or acceleration proportional to its displacement. This motion is characterized by a sinusoidal wave-like pattern. Since it repeats itself over time, it is inherently periodic.

Option 3 states that there is no correlation between simple harmonic motion and the periodicity of motion. This statement is incorrect, as simple harmonic motion is a specific type of periodic motion.

Option 4 suggests that the relation between simple harmonic motion and periodic motion depends on the mass of the object undergoing the motion. This statement is not accurate since the relation between simple harmonic motion and periodic motion is mainly determined by the type of motion and the restoring force acting on the object, rather than the mass.

Therefore, the correct answer is option 2, which states that all simple harmonic motions are necessarily periodic motions.