A steel meter scale is to be ruled so that millimeter intervals are accurate within about $5 \times 10^{-5}$ $mm$ at a certain temperature. The maximum temperature variation allowable during the ruling is .......... $^oC$  (Coefficient of linear expansion of steel $ = 10 \times {10^{ - 6}}{K^{ - 1}})$

A steel tape gives correct measurement at $20^o C$. A piece of wood is being measured with the steel tape at $0^o C$. The reading is $25 \,\,cm$ on the tape, the real length of the given piece of wood must be:

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} ) $

A thin walled cylindrical metal vessel of linear coefficient of expansion $10^{-3} $ $^o C^{-1}$ contains benzenr of volume expansion coefficient $10^{-3}$ $^o C^{-1}$. If the vessel and its contents are now heated by $10^o C,$ the pressure due to the liquid at the bottom.

Each side of a box made of metal sheet in cubic shape is $'a'$ at room temperature $'T'$, the coefficient of linear expansion of the metal sheet is $^{\prime} \alpha^{\prime}$. The metal sheet is heated uniformly, by a small temperature $\Delta T$, so that its new temperature is $T +\Delta T$. Calculate the increase in the volume of the metal box.

An aluminium sphere of $20 \;cm$ diameter is heated from $0^{\circ} C$ to $100^{\circ} C$. Its volume changes by (given that coefficient of linear expansion for aluminium $\alpha_{A l}=23 \times 10^{-6}\;/{^o}C$