Under the same load, wire A having length 5.0 m and cross section stretches uniformly by the same amount as another wire B of length 6.0 m and a cross section of stretches. The ratio of the Young’s modulus of wire A to that of wire B will be

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Solution

Q.
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 [2023]

1 1 : 4

2 1 : 1

3 1 : 10

4 1 : 2

Ans.
(2)

$Δ l = \frac{F l}{S Y}$

$Since F is same for both wires and Δ l is also same$

$\frac{Δ l}{F} = \frac{l}{S Y} \Rightarrow \frac{l_{A}}{S_{A} Y_{A}} = \frac{l_{B}}{S_{B} Y_{B}}$

$\Rightarrow \frac{5}{2.5 \times Y_{A}} = \frac{6}{3 \times Y_{B}}$

$\Rightarrow \frac{Y_{A}}{Y_{B}} = 1$

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