JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Elasticity & SHM

A rod of length

L

at room temperature and uniform area of cross section

A

, is made of a metal having coefficient of linear expansion

α /^{\circ} C

. It is observed that an external compressive force F, is applied on each of its ends, prevents any change in the length of the rod, when it temperature rises by

Δ TK

. Young's modulus, Y , for this metal is

(A) $\frac{F}{A α Δ T}$ ✓ Correct
(B) $\frac{F}{A α ( Δ T - 273 )}$
(C) $\frac{F}{2 A α Δ T}$
(D) $\frac{2 F}{A α Δ T}$

Answer: (A)

Solution

If the rod were free it would lengthen by

Δ L = Lα Δ T

, so the thermal strain it is prevented from taking is

ε = α Δ T

. The external force supplies the compressive stress

σ = \frac{F}{A}

that holds it back. Young's modulus is stress over strain,

Y = \frac{F / A}{α Δ T} = \frac{F}{A α Δ T}

JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Single correct option

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JEE Main · 2019 · 09 Jan 2019 · Shift 1 · Elasticity & SHM

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