Two rods of different materials having coefficients of linear expansion α1 and α2 and Young’s moduli, Y1 and Y2, respectively…

Q: Two rods of different materials having coefficients of linear expansion α1 and α2 and Young’s moduli, Y1 and Y2 respectively, are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If α12 = 2/3, then the thermal stresses developed in the two rods are equal provided Y1/Y2 is equal to

(a) 2 : 3

(b) 1 : 1

(c) 3 : 2

(d) 4 : 9

Ans: (c)

Sol:

\displaystyle Y_1 \alpha_1 \Delta \theta = Y_2 \alpha_2 \Delta \theta

\displaystyle Y_1 \alpha_1  = Y_2 \alpha_2

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

\displaystyle \frac{Y_1}{Y_2} = \frac{3}{2}

A uniform pressure ‘P’ is exerted on all sides of a solid cube at temperature 0°C. In order to bring…

Q: A uniform pressure ‘P’ is exerted on all sides of a solid cube at temperature 0°C. In order to bring the volume of the cube to the original volume, the temperature of the cube must be increased by t°C. If α is the linear coefficient and K be the bulk modulus of the material of the cube, then t is equal to

(a) \displaystyle \frac{3P}{K \alpha}

(b) \displaystyle \frac{P}{2 K \alpha}

(c) \displaystyle \frac{P}{3 K \alpha}

(d) \displaystyle \frac{P}{K \alpha}

Ans: (c)