A constrained steel rod of length \(l\), area of cross-section \(A\), Young's modulus \(Y\) and coefficient of linear expansion \(\alpha\)$$ is heated through \(t^{\circ}\text{C}\)$$. The work that can be performed by the rod when heated is:
1. \((YA\alpha t)(l\alpha t)\)
2. \(\frac{1}{2}(YA\alpha t)(l\alpha t)\)
3. \(\frac{1}{2}(YA\alpha t)\frac{1}{2}(l\alpha t)\)
4. \(2(YA\alpha t)(l\alpha t)\)

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 the coefficient of linear expansion is \(\alpha\). If the temperature of the rod is increased by \(\Delta t^{\circ} \mathrm{C}\), the force exerted by the rod on the supports will be:
1. \(YAL\Delta t\)
2. \(YA\alpha\Delta t\)
3. \(\frac{YL\alpha\Delta t}{A}\)
4. \(Y\alpha AL\Delta t\)

A rod of length 40 cm is stretched between two rigid supports at zero tension. If the temperature is increased by 10°C, the stress produced in it is:

(Young's modulus, Y = 1.2x${10}^{12} \mathrm{N}/{\mathrm{m}}^2$, coefficient of linear expansion of rod = 2 x ${10}^{-5}$/°C)

(1) 2.4 x ${10}^8 \mathrm{N}/{\mathrm{m}}^2$

(2) 1.2 x ${10}^8 \mathrm{N}/{\mathrm{m}}^2$

(3) 3.6 × ${10}^8 \mathrm{N}/{\mathrm{m}}^2$

(4) 4.8 x ${10}^8 \mathrm{N}/{\mathrm{m}}^2$

An aluminum rod of length 2m held fixed in a horizontal position from its one end has the other end free. When the temperature of rod increases by 100°C, the thermal stress produced in the rod will be ($\mathrm{\alpha }$ = 1.6 x ${10}^{-6}$/°C)

(1) Zero

(2) 0.08

(3) 0.1

(4) 0.4

The metal rod (Y = 2 x ${10}^{12}$ dyne/sq. cm) of the coefficient of linear expansion 1.6 x ${10}^{-5}$ per °C has its temperature raised by 20°C. The linear compressive stress to prevent the expansion of the rod is:

(1) 2.4 x ${10}^8$ dyne/sq. cm

(2) 3.2 x ${10}^8$ dyne/sq. cm

(3) 6.4 x ${10}^8$ dyne/sq. cm

(4) 1.6 x ${10}^8$ dyne/sq. cm