Question

Two rods of different materials having coefficient of thermal expansion a, and a, and Young's modulus '1 and
Y, respectively are fixed between two rigid massive walls. The rods are heated such that these undergo same
increase in temperature. There is no bending of the rods. If an: An = 2: 3, the thermal stress developed in
the two rods are equal, provided Y: Y2 is​

Answer 1

Answer:

Ratio of Young's Modulus of two rods is 3 : 2

Explanation:

As we know that stress on the rod is given as

stress = (Young's modulus)(Strain)

Now we know that when temperature of the rod is increased then its extension in the length is given as

$\Delta L = L\aplha \Delta T$

so strain in the rod due to increase in temperature is given as

$\frac{\Delta L}{L} = \alpha \Delta T$

now thermal stress on the rod is given as

$stress = Y\alpha \Delta T$

Now given that the thermal stress in two rods are equal so we have

$Y_1\alpha_1\Delta T = Y_2\alpha_2\Delta T$

so we have

$\frac{Y_1}{Y_2} = \frac{\alpha_2}{\alpha_1}$

so we know that

$\alpha_1 : \alpha_2 = 2 : 3$

so we have

$Y_1 : Y_2 = 3 : 2$

#Learn

Topic : Thermal Stress

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Answer 2

Answer:

3:2

Explanation:

see the above attachment

see the above attachmentHope you get it ☺️✨