Find the ratio of the length of a steel rod and a copper rod if the steel rod is $4 \ cm$ longer than the copper rod at any temperature. $[$The coefficients of linear expansion for steel and copper are $1.1 \times 10^{-5} /^{\circ} C$ and $1.7 \times 10^{-5} /^{\circ} C$ respectively$]$

When the temperature of a body increases from $T$ to $T+\Delta T$, its moment of inertia increases from $I$ to $I+\Delta I$. If $\alpha$ is the coefficient of linear expansion of the material of the body, then $\frac{\Delta I}{I}$ is (neglect higher orders of $\alpha$ ).

$A$ silver rod of $100 \; cm$ at $0^{\circ} C$ is heated to $100^{\circ} C$. Its length increases by $0.19 \; cm$. The coefficient of cubical expansion of the silver rod is:

$A$ metal rod having a coefficient of linear expansion $2 \times 10^{-5} /{ }^{\circ} C$ is $0.75 \ m$ long at $45^{\circ} C$. When the temperature rises to $65^{\circ} C$,the increase in length of the rod will be: (in $mm$)

$A$ composite rod made up of two rods $AB$ and $BC$ are joined at $B$. The rods are of equal length at room temperature and have equal masses. The coefficient of linear expansion $\alpha$ of $AB$ is more than that of $BC$. The composite rod is suspended horizontally by means of a thread at $B$. When the rod is heated:

Two holes of unequal diameters $d_1$ and $d_2$ $(d_1 > d_2)$ are cut in a metal sheet. If the sheet is heated,then: