The temperature of a metal coin is increased by $100^{\circ} C$ and its diameter increases by $0.15 \%$. Its area increases by nearly (in $\%$)

$A$ rod of length $20 \, cm$ is made of metal $A$. It expands by $0.075 \, cm$ when its temperature is raised from $0^{\circ}C$ to $100^{\circ}C$. Another rod of a different metal $B$ having the same length expands by $0.045 \, cm$ for the same change in temperature. $A$ third rod of the same length is composed of two parts,one of metal $A$ and the other of metal $B$. This rod expands by $0.06 \, cm$ for the same change in temperature. The portion made of metal $A$ has the length ............. $cm$.

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

The ratio of linear expansivity to the coefficient of superficial expansion of a rectangular sheet of a solid is

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:

When a body is heated, then the maximum rise will be in its