Question

A metal bar of length $L$ and area of cross-section $A$ is clamped between two rigid supports. Its Young's modulus for the material of the rod is $Y$ and coefficient of linear expansion is $a$. If the temperature of the rod is increased by $\Delta t^{\circ }C$ the force exerted by the rod on the supports is QImg

• A. $YAL\Delta t$
• B. $YA\alpha \Delta t$
• C. $\frac{YA\alpha \Delta t}{A}$
• D. $Y\alpha A\Delta t$

Answer 1

Answer: (B)

Young?s elasticity coefficient $Y=\frac{Fl}{A\Delta l}$
According to definition of linear expansion coefficient
$\Delta l=\alpha l\Delta t$ where,
$l=$ initial length $Y=\frac{Fl}{A\alpha l\Delta t}$
or $Y=\frac{F}{A\alpha \Delta t}$
$F=YA\alpha \Delta t$ where,
$F=$ force applied on wire
$A=$ area of cross-section of wire
$\Delta t=$ increase in temperature of wire.