Final answer:
The breaking force for two parallel wires of the same thickness is 2F, and for a single wire of double the thickness is also 2F, making the correct answer D: (a) 2F, (b) 2F.
Step-by-step explanation:
The question concerns the breaking force of wires and how this force changes when multiple wires are used or when the thickness of a wire is changed. When two parallel wires of the same thickness are used, the breaking force doubles, since each wire can sustain a force F, resulting in a total force of 2F. However, when the thickness of a single wire is doubled, the breaking force also doubles since the cross-sectional area (which directly relates to strength) increases by a factor of four (since area is proportional to the square of the diameter), but the effect of the wire thickness on strength is subject to material properties and the actual geometry of the wire's cross-section.
Therefore, the correct answers are: (a) 2F for two parallel wires of the same thickness, and (b) 2F for a single wire of double the thickness. This corresponds to option D: (a) 2F, (b) 2F.