$A$ uniform copper rod of length $50 \,cm$ and diameter $3.0 \,mm$ is kept on a frictionless horizontal surface at $20^{\circ} C$. The coefficient of linear expansion of copper is $2.0 \times 10^{-5} \,K^{-1}$ and Young's modulus is $1.2 \times 10^{11} \,N/m^2$. The copper rod is heated to $100^{\circ} C$. The tension developed in the copper rod is .......... $\times 10^3 \,N$.

$A$ 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:

At some temperature $T$,a bronze pin is slightly too large to fit into a hole drilled in a steel block. The change in temperature required for an exact fit is minimum when:

When the temperature of a metal wire is increased from $0^{\circ} \,C$ to $10^{\circ} \,C$,its length increases by $0.02 \%$. The percentage change in its mass density will be closest to: (in $\%$)

$A$ steel tape $1 \; m$ long is correctly calibrated for a temperature of $27.0 \; ^{\circ}C$. The length of a steel rod measured by this tape is found to be $63.0 \; cm$ on a hot day when the temperature is $45.0 \; ^{\circ}C$. What is the actual length of the steel rod on that day? What is the length of the same steel rod on a day when the temperature is $27.0 \; ^{\circ}C$? (Coefficient of linear expansion of steel $\alpha = 1.20 \times 10^{-5} \; K^{-1}$)

Write the relation between the coefficient of linear expansion $(\alpha_l)$,coefficient of area expansion $(\alpha_A)$,and coefficient of volume expansion $(\alpha_V)$.