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

Calculate the stress developed inside a tooth cavity filled with copper when hot tea at temperature of $57\,^oC$ is drunk. You can take body (tooth) temperature to be $37\,^oC$ and $\alpha = 1.7 \times  10^{-5}/^oC$, bulk modulus for copper $ = 140 \times 10^9\, N/m^2 $.

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

Two rods are joined between fixed supports as shown in the figure. Condition for no change in the lengths of individual rods with the increase of temperature will be

( ${\alpha _1},\,{\alpha _2},$ = linear expansion coefficient

$A_1, A_2$ = Area of rods

$Y_1, Y_2$ = Young modulus)

Why the density is changed of solid substances by increase in temperature ?