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