$A$ rod of length $10 \, m$ at $0 \, ^oC$ has a linear expansion coefficient $\alpha = (2x^2 + 1) \times 10^{-6} \, ^oC^{-1}$,where $x$ is the distance from one end of the rod. The length of the rod at $10 \, ^oC$ is: (in $, m$)

$A$ non-isotropic solid metal cube has coefficients of linear expansion as:
$5 \times 10^{-5} /^{\circ} C$ along the $x$-axis and $5 \times 10^{-6} /^{\circ} C$ along the $y$ and the $z$-axis. If the coefficient of volume expansion of the solid is $C \times 10^{-6} /^{\circ} C$,then the value of $C$ is:

If the temperature of a rod is increased in such a way that no linear expansion occurs,then the stress developed in the rod does not depend on .......

The temperature of a metallic sphere of radius $R$ is increased by a small amount $\Delta T$. If the linear coefficient of thermal expansion of the metal is $\alpha$, the approximate increase in the volume of the sphere is :

$A$ seconds pendulum clock has a steel wire. The clock shows correct time at $25^{\circ} C$. How many seconds does the clock lose or gain in one week,when the temperature is increased to $35^{\circ} C$? (Given: $\alpha_{\text{steel}} = 1.2 \times 10^{-5} /^{\circ} C$)

The coefficient of apparent expansion of mercury in a glass vessel is $153 \times 10^{-6} \, ^{\circ}C^{-1}$ and in a steel vessel is $144 \times 10^{-6} \, ^{\circ}C^{-1}$. If $\alpha$ for steel is $12 \times 10^{-6} \, ^{\circ}C^{-1}$,then that of glass is: