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 $\%$)

$A$ thin copper wire of length $l$ meters is heated by $10^{\circ}C$,resulting in a $2\%$ increase in its length. If a square copper sheet of side $l$ meters is heated by the same $10^{\circ}C$,what is the percentage change in its area?

The linear expansion coefficients of brass and steel wires are $\alpha_1$ and $\alpha_2$ respectively,and their lengths at $0^\circ C$ are $L_1$ and $L_2$. If the difference $(L_2 - L_1)$ remains constant at any temperature,then:

$A$ circular metallic ring of radius $R$ has a small gap of width $d$. The coefficient of thermal expansion of the metal is $\alpha$. If we increase the temperature of the ring by an amount $\Delta T$,then the width of the gap:

The difference in length between two rods $A$ and $B$ is $60 \ cm$ at all temperatures. If $\alpha_A = 18 \times 10^{-6} /^{\circ}C$ and $\alpha_B = 27 \times 10^{-6} /^{\circ}C$,then the lengths of rod $A$ and rod $B$ at $0^{\circ}C$ are respectively:

$A$ solid rectangular sheet has two different coefficients of linear expansion $\alpha_{1}$ and $\alpha_{2}$ along its length and breadth respectively. The coefficient of surface expansion is (for $\alpha_{1} \Delta t \ll 1, \alpha_{2} \Delta t \ll 1$):