$A$ 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 $= 10^{-5} /{ }^{\circ} C$)

When the temperature of a metal wire is increased from $0^{\circ} \,C$ to $10^{\circ} \,C$,its length increases by $0.02 \%$. The percentage change in its mass density will be closest to: (in $\%$)

$A$ 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 $= 1.2 \times 10^{-5} \ ^{\circ} C^{-1}$).

The coefficient of linear expansion of a crystal in one direction is ${\alpha _1}$ and that in every direction perpendicular to it is ${\alpha _2}$. The coefficient of cubical expansion is

When a meter rod made of silver at $0^{\circ} C$ is heated to $100^{\circ} C$,its length increases by $0.19 \ cm$. Find the coefficient of volume expansion of the silver.

Two rods of different materials have lengths $\ell_1$ and $\ell_2$ whose coefficients of linear expansion are $\alpha_1$ and $\alpha_2$ respectively. If the difference between the two lengths is independent of temperature,then: