The pressure to be applied to the ends of a steel cylinder to keep its length constant upon raising its temperature by $100^{\circ} C$ is (thermal expansion coefficient, $\alpha = 11 \times 10^{-6} / K$, Young's modulus $Y = 200 \text{ GPa}$)

$A$ rod is fixed between two points at $20\,^oC$. The coefficient of linear expansion of the material of the rod is $1.1 \times 10^{-5}/\,^oC$ and Young's modulus is $1.2 \times 10^{11}\,N/m^2$. Find the stress developed in the rod if the temperature of the rod becomes $10\,^oC$.

The length of an elastic string is $x \, m$ when the tension is $8 \, N$ and $y \, m$ when the tension is $10 \, N$. The length in meters when the tension is $18 \, N$ is:

$A$ uniform rod of length $L$ is rotated in a horizontal plane about a vertical axis through one of its ends. The angular speed of rotation is $\omega$. Find the increase in length of the rod, if $\rho$ and $Y$ are the density and Young's modulus of the rod respectively.

$A$ wooden wheel of radius $R$ is made of two semicircular parts. The two parts are held together by a metal ring of cross-sectional area $S$ and length $L$. $L$ is slightly less than $2\pi R$. To fit the ring on the wheel,the ring is heated by a temperature $\Delta T$. If the coefficient of linear expansion of the metal is $\alpha$ and its Young's modulus is $Y$,the force that one part of the wheel exerts on the other is:

Two wires of the same length and radius are joined end-to-end and loaded. The Young's moduli of the materials of the two wires are $Y_{1}$ and $Y_{2}$. If the combination behaves as a single wire,then its equivalent Young's modulus is: