Two uniform brass rods $A$ and $B$ of length $l$ and $2l$ and their radii $2r$ and $r$ respectively are heated to the same temperature. The ratio of the increase in the volume of rod $A$ to that of rod $B$ is

At a certain temperature,rod $A$ and rod $B$ of different materials have lengths $L_A$ and $L_B$ respectively. Their coefficients of linear expansion are $\alpha_A$ and $\alpha_B$ respectively. It is observed that the difference between their lengths remains constant at all temperatures. The ratio $L_A / L_B$ is given by

The density of a substance at $0 \, ^\circ C$ is $10 \, g/cm^3$ and at $100 \, ^\circ C$ is $9.7 \, g/cm^3$. The coefficient of linear expansion of the substance is ..... $^\circ C^{-1}$.

$A$ 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 .......... $\times 10^3 \,N$.

Three rods of equal lengths are joined to form an equilateral triangle $ABC$. $D$ is the mid-point of $AB$. The coefficient of linear expansion is $\alpha_1$ for the material of rod $AB$ and $\alpha_2$ for the material of rods $AC$ and $BC$. If the distance $DC$ remains constant for small changes in temperature, then:

$A$ metal rod of silver at $0^{\circ}C$ is heated to $100^{\circ}C$. Its length increases by $0.19\, cm$. If the original length of the rod is $100\, cm$,the coefficient of cubical expansion of the silver rod is: