NEET 2024 — Physics solution

NEET2024Physics

A metallic bar of Young's modulus, $0.5 \times 1 0^{11}$ Nm $^{- 2}$ and coefficient of linear thermal expansion $1 0^{- 5}^{\circ}$ C $^{- 1}$ , length 1 m and area of cross-section $1 0^{- 3}$ m $^{2}$ is heated from 0 $^{\circ}$ C to 100 $^{\circ}$ C without expansion or bending. The compressive force developed in it is:

A
$100 \times 1 0^{3}$ N
B
$2 \times 1 0^{3}$ N
C
$5 \times 1 0^{3}$ N
D
$50 \times 1 0^{3}$ N

Solution

If expansion is prevented, the bar develops a thermal stress $σ = Y α Δ T$ .

Force $F = σ A = Y α A Δ T = 0.5 \times 1 0^{11} \times 1 0^{- 5} \times 1 0^{- 3} \times 100 = 50 \times 1 0^{3}$ N.

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