$A$ metal tape is calibrated at $25^{\circ} C$. On a cold day when the temperature is $-15^{\circ} C$,the percentage error in the measurement of length is (Coefficient of linear expansion of metal $= 1 \times 10^{-5} {}^{\circ} C^{-1}$) (in $\%$)

The temperature of a metallic sphere of radius $R$ is increased by a small amount $\Delta T$. If the linear coefficient of thermal expansion of the metal is $\alpha$, the approximate increase in the volume of the sphere is :

To increase the length of a metal rod by $0.4 \%$, the temperature of the rod is to be increased by (Coefficient of linear expansion of the metal $= 20 \times 10^{-6} \ {}^{\circ}C^{-1}$) (in $K$)

Two rods,one made of aluminium and the other made of steel,having initial lengths $l_1$ and $l_2$ respectively,are connected together to form a single rod of length $(l_1 + l_2)$. The coefficients of linear expansion for aluminium and steel are $\alpha_1$ and $\alpha_2$ respectively. If the length of each rod increases by the same amount when their temperature is raised by $t^oC$,then the ratio $l_1/(l_1 + l_2)$ is:

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

$A$ composite rod made up of two rods $AB$ and $BC$ are joined at $B$. The rods are of equal length at room temperature and have equal masses. The coefficient of linear expansion $\alpha$ of $AB$ is more than that of $BC$. The composite rod is suspended horizontally by means of a thread at $B$. When the rod is heated: