$A$ metal rod $2 \,m$ long increases in length by $1.6 \,mm$, when heated from $0^{\circ} C$ to $60^{\circ} C$. The coefficient of linear expansion of the metal rod is:

The volume of a metal sphere increases by $0.33 \%$ when its temperature is raised by $50^{\circ} C$. The coefficient of linear expansion of the metal is

The moment of inertia $I$ of a uniform rod about a perpendicular bisector increases to $I+\Delta I$, if the temperature is increased slightly by $\Delta T$. If the coefficient of linear expansion is $\alpha$, then $\frac{\Delta I}{I}$ is (Assume $\frac{\Delta T}{T} \ll 1$)

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:

Three rods of equal lengths are joined to form an equilateral triangle $ABC$. $D$ is the mid-point of $AB$. The coefficient of linear expansion is $\alpha_1$ for the material of rod $AB$ and $\alpha_2$ for the material of rods $AC$ and $BC$. If the distance $DC$ remains constant for small changes in temperature, then:

$A$ bimetallic strip consists of metals $X$ and $Y$. It is mounted rigidly at the base as shown. The metal $X$ has a higher coefficient of linear expansion compared to that for metal $Y$. When the bimetallic strip is placed in a cold bath: