Coefficient of linear expansion of brass and steel rods are $\alpha_1$ and $\alpha_2$. Lengths of brass and steel rods are $l_1$ and $l_2$ respectively. If $\left(l_2-l_1\right)$ is maintained same at all temperatures, which one of the following relations holds good?

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 expansion compared to that for metal $Y$. When the bimetallic strip is placed in a cold bath:

A steel rail of length $5\,m$ and area of cross-section $40\,cm^2$ is prevented from expanding along its length while the temperature rises by $10\,^oC$. If coefficient of linear expansion and Young's modulus of steel are $1.2\times10^{-5}\, K^{-1}$ and $2\times10^{11}\, Nm^{-2}$ respectively, the force developed in the rail is approximately

A blacksmith fixes iron ring on the rim of the wooden wheel of a horse cart. The diameter of the rim and the iron ring are $5.243\; m$ and $5.231\; m$, respectively at $27^oC$. To what temperature (in $^oC$) should the ring be heated so as to fit the rim of the wheel?

A sphere of diameter $7\,\, cm$ and mass $266.5 \,\,gm$ floats in a bath of a liquid. As the temperature is raised, the sphere just begins to sink at a temperature $35^o C$. If the density of a liquid at $0^o C$ is $1.527 \,\,gm/cc$, then neglecting the expansion of the sphere, the coefficient of cubical expansion of the liquid is$f$ :

The length of a metallic rod is $5m$ at $0°C$ and becomes $  5.01\, m$, on heating upto $100°C$. The linear expansion of the metal will be