An iron tyre is to be fitted on to a wooden wheel 1m in diameter. The diameter of tyre is $6\, mm$ smaller than that of wheel. The tyre should be heated so that its temperature increases by a minimum of ........ $^oC$ (the coefficient of cubical expansion of iron is ${3.6 \times 10^{-5} } °C^{-1}$)

If on heating liquid through $80°C$, the mass expelled is $(1/100)^{th}$ of mass still remaining, the coefficient of apparent expansion of liquid is

A flask of volume $10^3 cc$ is completely filled with mercury at $0 ^oC$. The coefficient of cubical expansion of mercury is $180 × 10^{-6} / ^oC$ and that of glass is $40 × 10^{-6}/ ^oC$. If the flask is now placed in boiling water at $100\ ^oC$, ........ $cc$ mercury will overflow 

A bar of iron is $10\, cm$ at $20°C$. At $19°C$ it will be ($\alpha$ of iron $= 11 \times 10^{-6}/°C$)

A glass flask contains some mercury at room temperature. It is found that at different temperatures the volume of air inside the flask remains the same. If the volume of mercury in the flask is $300 \,\,cm^3$, then volume of the flask is ........ $cm^3$. (given that coefficient of volume expansion of mercury and coefficient of linear expansion of glass are $1.8 × 10^{-4} (^o C)^{-1}$ and $9 × 10^{-6} (^o C)^{-1}$ respectively)

Ratio among linear expansion coefficient ($\alpha$), areal expansion coefficient ($\beta$) and volume expansion coefficient ($\gamma$) is