A copper rod of $88\; \mathrm{cm}$ and an aluminum rod of unknown length have their increase in length independent of increase in temperature. The length of aluminum rod is....$cm$

$( \alpha_{Cu}=1.7 \times 10^{-5}\; \mathrm{K}^{-1}$ and $\alpha_{Al}=2.2 \times 10^{-5} \;\mathrm{K}^{-1} ) $

The coefficients of thermal expansion of steel and a metal $X$ are respectively $12 × 10^{-6}$ and $2 × 10^{-6} per^o C$. At $40^o C$, the side of a cube of metal $X$ was measured using a steel vernier callipers. The reading was $100 \,\,mm$.Assuming that the calibration of the vernier was done at $0^o C$, then the actual length of the side of the cube at $0^o C$ will be

A liquid with coefficient of volume expansion $\gamma$ is filled in a container of a material having the coefficient of linear expansion $\alpha$. If the liquid overflows on heating, 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 expansion compared to that for metal $Y$. When the bimetallic strip is placed in a cold bath:

A thin copper wire of length $L$ increase in length by $1\%$ when heated from temperature $T_1$ to $T_2$. What is the percentage change in area when a thin copper plate having dimensions $2L\times  L$ is heated from $T_1$ to $T_2$ ? ....... $\%$

On what value of $\alpha _l$ depends ? Write its unit.