JEE Main · 2026 · 05 Apr 2026 · Shift 1 · Elasticity & SHM

The Young's modulus of steel wire of radius

r

and length L is Y. If the radius r and length L of the wire are doubled then the value of Y

(A)increases by two times
(B)reduces by half
(C)remains unchanged✓ Correct
(D)becomes one fourth

Answer: (C)

Solution

Young's modulus

Y = \frac{stress}{strain} = \frac{F / A}{Δ L / L}

is a property of the material itself, set by its composition and temperature, not by the shape or size of the specimen. Doubling the radius and the length alters the wire's stiffness and its extension, but leaves the ratio of stress to strain unchanged. Young's modulus therefore remains unchanged.

JEE Main · 2026 · 05 Apr 2026 · Shift 1 · Single correct option

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