JEE Main 2026 — Jan 28, Shift 1 — Physics solution

JEE Main2026Jan 28, Shift 1Physics

Two wires $A$ and $B$ made of different materials of length 6.0 cm and 5.4 cm, respectively and area of cross sections $3.0 \times 1 0^{- 5}$ m $^{2}$ and $4.5 \times 1 0^{- 5}$ m $^{2}$ , respectively are stretched by the same magnitude under a given load. The ratio of the Young's modulus of $A$ to that of $B$ is $x : 3$ . The value of $x$ is ______ .

Solution

Young's modulus $Y = \frac{F ℓ}{A Δ ℓ}$ . Same load $F$ and same extension $Δ ℓ$ on both wires, so

$\frac{Y _{A}}{Y _{B}} = \frac{ℓ _{A}}{ℓ _{B}} \cdot \frac{A _{B}}{A _{A}} = \frac{6.0}{5.4} \cdot \frac{4.5 \times 1 0 ^{- 5}}{3.0 \times 1 0 ^{- 5}} = \frac{6}{5.4} \cdot \frac{1.5}{1} = \frac{9}{5.4} = \frac{5}{3}$ .

$∴ x = 5$ . Option (4).

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