Question 6

Under the same load, wire A having length 5.0 m and cross section $$2.5 \times 10^{-5}$$ m$$^2$$ stretches uniformly by the same amount as another wire B of length 6.0 m and a cross section of $$3.0 \times 10^{-5}$$ m$$^2$$ stretches. The ratio of the Young's modulus of wire A to that of wire B will be:

Solution

Wire A: length $$L_A = 5.0$$ m, cross-section $$A_A = 2.5 \times 10^{-5}$$ m².

Wire B: length $$L_B = 6.0$$ m, cross-section $$A_B = 3.0 \times 10^{-5}$$ m².

Same load $$F$$, same extension $$\Delta L$$.

Young's modulus formula:

$$Y = \frac{F \cdot L}{A \cdot \Delta L}$$

Ratio:

$$\frac{Y_A}{Y_B} = \frac{L_A / A_A}{L_B / A_B} = \frac{L_A \times A_B}{L_B \times A_A}$$ $$= \frac{5.0 \times 3.0 \times 10^{-5}}{6.0 \times 2.5 \times 10^{-5}} = \frac{15}{15} = 1$$

So $$Y_A : Y_B = 1 : 1$$.

The answer is Option B: 1 : 1.

Solution

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