A wire of area of cross-section 'A' and original length 'l' is subjected to a load 'L'. A second wire of the same material with an area is '2A' and a length of '2l' is subjected to the same load 'L'. If the extension in the first wire is 'X' and the second wire is 'Y', find the ratio 'X/Y'.
Correct answer: C. 1:1
- A. 1:4
- B. 1:2
- C. 1:1
- D. 2:1
Explanation
To determine the correct ratio, we can use the formula for the extension of a wire under an applied load, which is given by Hooke's Law:Extension (ΔL) = (Load (L) * Length (l)) / (Area of Cross Section (A) * Young's Modulus (E))For the first wire: X = (L * l) / (A * E)For the second wire: Y = (L * 2l) / (2A * E)By simplifying the expressions, we find that X = Y, which means the extension in the first wire is equal to the extension in the second wire. Therefore, the correct ratio is 1:1.Hence, the correct option is c) 1:1, which represents the ratio of X/Y as 1:1.
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