A metal bar of length L and area of cross-section A is clamped between two rigid supports. For the material of the rod, its Young’s modulus is Y and coefficient of linear expansion is $\alpha$ . If the temperature of the rod is increased by $\Delta t^{\circ}C,$ the force exerted by the rod on the supports is
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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 $\mathrm{Y} = \frac{\mathrm{F}}{\mathrm{A} \alpha \Delta t}$
$\mathbf{F} = Y A \alpha \Delta t$ where,
$\mathbf{F}=$ force applied on wire
$A=$ area of cross-section of wire
$\Delta t$ increase in temperature of wire.
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