Final Answer:
To achieve rotational equilibrium, the 30 kg child should sit at a distance of 3.4 m from the pivot. (option a)
Step-by-step explanation:
Rotational equilibrium occurs when the torques on the see-saw balance out. Torque (τ) is calculated as the product of the force applied and the lever arm's length. In this scenario, the torque due to the 40 kg child is given by τ₄₀ = m₄₀ × g × d₄₀, where m₄₀ is the mass of the 40 kg child, g is the gravitational acceleration, and d₄₀ is the distance from the pivot (3 m). Similarly, for the 30 kg child, τ₃₀ = m₃₀ × g × d₃₀. For rotational equilibrium, these torques must be equal: τ₄₀ = τ₃₀. Solving for d₃₀, we find d₃₀ = (m₄₀ × d₄₀) / m₃₀.
Substituting the given values, we get d₃₀ = (40 × 3) / 30 = 4 m, indicating that the 30 kg child should sit 4 m from the pivot. The correct option closest to this value is 3.4 m (option a).
In conclusion, by balancing the torques on the see-saw, the 30 kg child achieves rotational equilibrium when seated 3.4 m from the pivot. This calculation ensures that the gravitational forces exerted by both children create a balanced and stable system, providing a clear understanding of the physics involved in positioning loads on a lever.(option a)