A steel rod of length L and diameter D- fixed at both ends- is uniformly heated to a temperature rise of - T- The Young-s modulus is E and the coefficient of linear expansion is - The thermal stress in the rod is

Thermal strain, ε _t = Change in length prevented/Original length = LαΔ TL = αΔ T Thremal stress, nbsp;σ _t = ε _t × E = αΔ TE nbsp; ...

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Standard VII

Physics

Young's Modulus of Elasticity

A steel rod o...

Question

A steel rod of length L and diameter D, fixed at both ends, is uniformly heated to a temperature rise of $Δ T$ . The Young's modulus is E and the coefficient of linear expansion is $α$ . The thermal stress in the rod is

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α Δ T

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E α Δ T

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E α Δ T L

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Solution

The correct option is C $E α Δ T$

Thermal strain,
$ε_{t} = \frac{C h a n g e i n l e n g t h p r e v e n t e d}{O r i g i n a l l e n g t h} = \frac{L α Δ T}{L} = α Δ T$
Thremal stress, $σ_{t} = ε_{t} \times E = α Δ T E$

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A steel rod of length L and diameter D, fixed at both ends, is uniformly heated to a temperature rise of ΔT. The Young's modulus is E and the coefficient of linear expansion is α. The thermal stress in the rod is

The correct option is C EαΔT Thermal strain, εt = Change in length preventedOriginal length = LαΔTL = αΔT Thremal stress, σt = εt × E = αΔTE

A steel rod of length L and diameter D, fixed at both ends, is uniformly heated to a temperature rise of $Δ T$ . The Young's modulus is E and the coefficient of linear expansion is $α$ . The thermal stress in the rod is

The correct option is C $E α Δ T$

Thermal strain,
$ε_{t} = \frac{C h a n g e i n l e n g t h p r e v e n t e d}{O r i g i n a l l e n g t h} = \frac{L α Δ T}{L} = α Δ T$
Thremal stress, $σ_{t} = ε_{t} \times E = α Δ T E$