Question

A compressive force, F is applied at the two ends of a long thin steel rod. It is hated, simultaneously, such that its temperature increases by $△T$ . The net change in its length is zero. Let l be the length of the rod, A its area of cross-section, Y its Young,s modulus, and $\alpha$ its coefficient of linear expansion. Then, F is equal to :

• A. $l^{2}Y\alpha △T$
• B. $lAY\alpha △T$
• C. $\frac{AY}{\alpha △T}$
• D. $AY\alpha △T$

Answer 1

$\frac{\Delta L}{L}=\alpha \Delta T$

$\frac{Stress}{Strain}=Y$

$\frac{F}{A\alpha \Delta T}=Y$

$\frac{F}{A}=Y\alpha \Delta T$

$F=AY\alpha \Delta T$