A metallic tape gives correct value at $25^{\circ} C$. A piece of wood is being measured by this metallic tape at $10^{\circ} C$. The reading is $30 \,cm$ on the tape, the real length of wooden piece must be .......... $cm$

If the length of a cylinder on heating increases by $2\%$, the area of its base will increase by ....... $\%$

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:

The gap between any two rails, each of length $l$ laid on a railway track equal $x$ at $27\,^oC$ . When the temperature rises to $40\,^oC$ , the gap close up. The coefficient of linear expansion of the material of the rail is $\alpha $ . The length $l$ of a rail at $27\,^oC$ will be

A solid ball of metal has a concentric spherical cavity within it. If the ball is heated, the volume of the cavity will

An iron bar of length $10\, m$ is heated from $0°C$ to $100°C.$ If the coefficient of linear thermal expansion of iron is $ 10 \times 10^{-6}{°C^{-1}}$, the increase in the length of bar is  .......... $cm$