Two wires A and B are of same materials. Their lengths are in the ratio 1:2 and diameters are in the ratio 2:1. When stretched by forces \(F_A\) and \(F_B\) respectively, they get equal increase in their lengths. Then the ratio \(F_A : F_B\) should be
Show Hint
- 1:2
- 1:1
- 2:1
- 8:1
The Correct Option is D
Solution and Explanation
\(Y = \frac{FL}{A \Delta L}\), so \(F \propto \frac{A}{L}\).
Step 2: Detailed Explanation:
\(\frac{F_A}{F_B} = \frac{A_A}{A_B} \times \frac{L_B}{L_A}\)
\(A \propto d^2 \rightarrow \frac{A_A}{A_B} = \left(\frac{2}{1}\right)^2 = 4\)
\(\frac{L_B}{L_A} = \frac{2}{1} = 2\)
\(\frac{F_A}{F_B} = 4 \times 2 = 8\)
Step 3: Final Answer:
Ratio is 8:1.
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