First slide

Elastic Modulie

Question

An iron rod $(Y = 10^{11} N / m^{2}, α = 10^{- 5} /^{\circ} C)$ has a length of one metre and cross-section 10cm². By raising its temperature from 0°c to 100°C and holding it so that it is not permitted to expand or bend, the force developed is

Moderate

A

10⁹N
B

10⁵N
C

10⁴N
D

10³N

Solution

$Y = \frac{(F / A)}{(l / L)} or F = \frac{YAl}{L}$
Further $l = Lαt (t = temperature rise)$
$\begin{array}{l} ∴ F = \frac{YALαt}{L} = YAαt \\ = 10^{11} \times (10 \times 10^{- 4}) \times 10^{- 5} \times 100 = 10^{5} N \end{array}$

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