Final answer:
The moment of inertia of the system is found by summing the products of each particle's mass and the square of its distance from the y-axis, totaling to 21 kg · m², not 3 Nm² as mentioned in the question.
Step-by-step explanation:
The problem asks us to find the moment of inertia of a system of particles about the y-axis. The particles each have a mass of 1 kg and are positioned at 1 m, 2 m, and 4 m on the x-axis from the origin. The moment of inertia (I) is the sum of the product of each mass (m) and the square of its distance (r) from the axis of rotation. The formula is I = Σm·r².
In this system, using the formula and given positions:
- For the particle at 1 m: I1 = 1 kg × (1 m)² = 1 kg · m²
- For the particle at 2 m: I2 = 1 kg × (2 m)² = 4 kg · m²
- For the particle at 4 m: I3 = 1 kg × (4 m)² = 16 kg · m²
Thus, the total moment of inertia of the system about the y-axis is I = I1 + I2 + I3 = 1 + 4 + 16 = 21 kg · m². Since the question mentions that the moment of inertia is 3 Nm², it appears there is a discrepancy, as the correct calculation yields 21 kg · m² instead.