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 $\%$)

$A$ metal rod of length $20 \, cm$ expands by $0.075 \, cm$ when its temperature is raised from $0 \, ^\circ C$ to $100 \, ^\circ C$. Another rod $B$ of a different metal of the same length expands by $0.045 \, cm$ for the same rise in temperature. $A$ third rod of the same length is composed of two metals $A$ and $B$ joined together. This composite rod expands by $0.060 \, cm$ for the same temperature difference. The length of the portion of metal $A$ is ..... $cm$.

The coefficient of apparent expansion of mercury in a glass vessel is $153 \times 10^{-6} /{ }^{\circ} C$ and in a steel vessel is $144 \times 10^{-6} /{ }^{\circ} C$. If $\alpha$ for steel is $12 \times 10^{-6} /{ }^{\circ} C$, then the coefficient of linear expansion $\alpha$ for glass is:

$A$ cylindrical metal rod of length $L_0$ is shaped into a ring with a small gap as shown. On heating the system,

The area of cross-section of a railway track is $0.01\, m^2$. The temperature variation is $10^{\circ}C$. The coefficient of linear expansion of the material of the track is $10^{-5} /^{\circ}C$. The energy stored per meter in the track is ...... $J/m$. (Young's modulus of the material of the track is $10^{11}\, Nm^{-2}$)

What must be the lengths of steel and copper rods at $0^o C$ for the difference in their lengths to be $10\,cm$ at any common temperature? $(\alpha_{steel}=1.2 \times 10^{-5} \;^o C^{-1})$ and $(\alpha_{copper} = 1.8 \times 10^{-5} \;^o C^{-1})$