Final answer:
The relationship between load and width of a beam is L = kW, and for the example provided, torque can be found using τ = rmg.
Step-by-step explanation:
The question is about the relationship between the load a beam can support and its width. If the load varies jointly as the width, then the relationship can be represented by the equation L = kW, where k is a constant proportionality factor. The correct answer is a) L = kW, where k is a constant.
To directly address the example provided regarding the horizontal beam: the torque τ about the support at the wall can be calculated using τ = r × F, where r is the distance from the pivot to the point of force application and F is the force. For a mass m at a distance r, the force due to gravity is F = mg, so the torque would be τ = rmg. In the case of the beam with length 3 m and a mass at the end, the torque would specifically be τ = 3m × g × 1.0 kg, considering standard acceleration due to gravity g.