JEE Main 2025 Apr 7 Shift 1, Physics Q19: Properties of Solids

JEE Main2025Apr 7, Shift 1Physics

Two wires A and B are made of same material having ratio of lengths $\frac{L _{A}}{L _{B}} = \frac{1}{3}$ and their diameters ratio $\frac{d _{A}}{d _{B}} = 2$ . If both the wires are stretched using same force, what would be the ratio of their respective elongations?

A
$1 : 6$
B
$1 : 12$
C
$3 : 4$
D
$1 : 3$

Solution

Elongation of a uniform wire under tension: $Δ L = \frac{F L}{A Y}$ .

With equal force and equal Young's modulus (same material), the ratio simplifies to

$\frac{Δ L _{A}}{Δ L _{B}} = \frac{L _{A}}{L _{B}} \cdot \frac{A _{B}}{A _{A}} = \frac{L _{A}}{L _{B}} \cdot (\frac{d _{B}}{d _{A}})^{2}$

Plug in the given ratios:

$\frac{Δ L _{A}}{Δ L _{B}} = \frac{1}{3} \cdot (\frac{1}{2})^{2} = \frac{1}{3} \cdot \frac{1}{4} = \frac{1}{12}$

$∴$ Option (2).

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JEE Main 2025 Apr 7 Shift 1, Physics Q19: Properties of Solids

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