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Shear Stress

A steel rod o...

Question

A steel rod of length 1 m is heated from $25^{\circ}$ to $75^{\circ}$ C keeping its length
constant. The longitudinal strain developed in the rod is (Given coefficient of linear expansion of steel $= 12 \times 10^{- 6} /^{\circ} C$ )

6 \times 10^{- 4}

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- 6 \times 10^{- 5}

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- 6 \times 10^{- 4}

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Solution

The correct option is C $- 6 \times 10^{- 4}$
Steel Rod of 1m
$T_{i} = 25^{\circ} C$ $T_{f} = 75^{\circ} C$
$l_{f} = l_{i} (1 + α Δ T)$
$l_{f} = 1 (1 + 12 \times 10^{- 6} \times 50)$
$l_{f} = 1 (1 + 6 \times 10^{- 4})$
but its still 1 m
So, strain developed $= \frac{Δ l}{l}$
$Δ l = - 6 \times 10^{- 4}$

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