Question

A metallic rod $l$ cm long, A square cm in cross-section is heated through $t^{\circ }$C. If Young's modulus of elasticity of the metal is E and the mean coefficient of linear expansion is $\alpha$ per degree 'celsius, then the compressional force required to prevent the rod from expanding along its length is:

• A. $EA\alpha t$
• B. $EA\alpha t/(1+\alpha t)$
• C. $EA\alpha t/(1-\alpha t)$
• D. $El\alpha t$

Answer 1

The correct option is A $EA\alpha t$

$Youn{g}^{\prime }smodulus=stress/strain$

i.e., $E=\frac{F/A}{\Delta l/l}=\frac{F/A}{\alpha t}$ $\Rightarrow F=EA\alpha t$