Question

A metal beam having coefficient of linear expansion $\alpha$ Youngs modulus $Y$ , area of across section a and length L, is clamped at both ends. After cooling by $t{}^\circ C,$ the force exerted in the clamp is

• A. $YL\alpha t$
• B. $Y\alpha a$
• C. $YaL\alpha t$
• D. $Ya\alpha t$

Answer 1

Answer: (D)

$Ya\alpha t$

Answer 2

: $Y=\frac{F}{a}\times \frac{L}{l}$ where a = area or $F=Yal/L$ ................ (i) $\alpha =\frac{Change\text{ }in\text{ }length\,(l)}{original\text{ }length(L)\times temperature\text{ }change(l)}$ or $\alpha =\frac{l}{Lt}$ .................. (ii) $\therefore$ $F=Ya\alpha t.$