$A$ metal metre scale that is accurate up to $0.5 \ mm$ is made at a temperature of $25^{\circ} C$. The range of temperatures within which it can be used is (Coefficient of linear expansion of the metal $= 10^{-5} /{ }^{\circ} C$)

$A$ uniform rod of length $L$ pivoted at one end $P$ is freely rotated in a horizontal plane with an angular velocity $\omega$ about a vertical axis passing through $P$. If the temperature of the system is increased by $\Delta T$, the angular velocity becomes $\frac{\omega}{2}$. If the coefficient of linear expansion of the rod is $\alpha$ (where $\alpha \ll 1$), then $\Delta T$ will be:

$A$ blacksmith fixes a circular iron frame on the wooden wheel of a bullock cart. The diameters of the wooden wheel and the circular iron frame are $5.012 \ m$ and $5 \ m$ respectively at $27^{\circ} C$. The temperature (in $^{\circ} C$) to which the iron ring must be heated so as to fit the wooden wheel is (Coefficient of linear expansion of iron $= 1.2 \times 10^{-5} \ ^{\circ} C^{-1}$).

What must be the lengths of steel and copper rods at $0^o C$ for the difference in their lengths to be $10\,cm$ at any common temperature? $(\alpha_{steel}=1.2 \times 10^{-5} \;^o C^{-1})$ and $(\alpha_{copper} = 1.8 \times 10^{-5} \;^o C^{-1})$

$A$ uniform copper rod of length $50 \,cm$ and diameter $3.0 \,mm$ is kept on a frictionless horizontal surface at $20^{\circ} C$. The coefficient of linear expansion of copper is $2.0 \times 10^{-5} \,K^{-1}$ and Young's modulus is $1.2 \times 10^{11} \,N/m^2$. The copper rod is heated to $100^{\circ} C$. The tension developed in the copper rod is .......... $\times 10^3 \,N$.

$A$ clock which keeps correct time at $20^{\circ} C$, is subjected to $40^{\circ} C$. If the coefficient of linear expansion of the pendulum is $12 \times 10^{-6} /{ }^{\circ} C$, how much time will it gain or lose per day?