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Answer :
Final answer:
The original length of the metallic wire when different tensions T1 and T2 are applied can be related by L1 = l2(T1/T2) based on Hooke's Law, showing a direct proportionality between the lengths L1 and l2 and the respective tensions T1 and T2.The correct option is a.
Explanation:
The question is related to the physics of materials, in particular, the relationship between the tension applied to a metallic wire and its length. When tension T1 is applied, the wire has length L1. When a different tension T2 is applied, its length changes to l2. To find the relationship between L1 and l2 given different tension values T1 and T2, we can use the principle that, for a perfectly elastic wire, the strain (which is proportional to the change in length) is directly proportional to the stress (which is proportional to the tension), provided we stay within the elastic limit.
From Hooke's Law, we know that the force (or tension) applied is directly proportional to the extensions it causes, as long as we do not exceed the material's elastic limit. We can frame this proportionality as L1 = l2 (T1/T2) if we assume that the wire returns to its original length once the tension is removed. This indicates that L1 is directly proportional to l2 when T2 is greater than T1, and inversely proportional when T1 is greater than T2.
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