Two wires of some nature have L2=3L1 and D1 = 3D2 for some extension F1/F2
Correct answer: D. 27 : 1
- A. 1 : 9
- B. 9 : 1
- C. 1 : 27
- D. 27 : 1
Explanation
The force ratio F1/F2 can be determined by considering the equation for the force required to cause a certain extension in a wire, which is proportional to its cross-sectional area and inversely proportional to its length. Given that L2 = 3L1 and D1 = 3D2, the cross-sectional area ratio A1/A2 is (D1/D2)2 = 9:1. Thus, the force ratio F1/F2 becomes (3L1L2) / (1/9) = 27:1. Therefore, option D is correct, as it accurately reflects these calculations. The other options do not correctly factorise the relationships between length, diameter, and force.
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