First slide

Thermal expansion

Question

What force should be applied to the ends of steel rod of a cross sectional area 10 $c m^{2}$ to prevent it from elongation when heated form 273 K to 303 k? (a of steel 10^-5 ° $C^{- 1}$ , Y = 2 × 10¹¹ Nm^-2 )

Moderate

A

2 × 10⁴N
B

3 × 10⁴N
C

6 × 10⁴N
D

12 × 10⁴ N

Solution

$Δ = \frac{Fl}{AY}$
$Increase in length, Δl = lαΔt$
$from (1) and (2); \frac{Fl}{AY} = l α Δt \Rightarrow F = YA α ΔT$

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