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

Given below are two statement : one is labelled as Assertion $A$ and the other is labelled as Reason $R$.

Assertion $A$ : When a rod lying freely is heated, no thermal stress is developed in it.

Reason $R :$ On heating the length of the rod increases.

In the light of the above statements, choose the correct answer from the options given below

A thin rod having length $L_0$ at $0\,^oC$ and coefficient of linear expansion $\alpha $ has its two ends maintained at temperatures  $\theta _1$ and $\theta _2$, respectively. Find its new length.

A bakelite beaker has volume capacity of $500\, cc$ at $30^{\circ} C$. When it is partially filled with $V _{ m }$ volume (at $30^{\circ}$ ) of mercury, it is found that the unfilled volume of the beaker remains constant as temperature is varied. If $\gamma_{\text {(beaker) }}=6 \times 10^{-6}{ }^{\circ} C ^{-1}$ and $\gamma_{(\text {mercury })}=1.5 \times 10^{-4}{ }^{\circ} C ^{-1},$ where $\gamma$ is the coefficient of volume expansion, then $V _{ m }($in $cc )$ is close to

A steel rod of diameter $1\,cm$ is clamped firmly at each end when its temperature is $25\,^oC$ so that it cannot contract on cooling. The tension in the rod at $0\,^oC$ is approximately ......... $N$ $(\alpha = 10^{-5}/\,^oC,\,\,Y = 2 \times 10^{11}\,N/m^2)$

On which of the following four processes, does the functioning of a bimetallic strip depends

$(i)$ Radiation

$(ii)$ Energy conversion

$(iii)$ Melting

$(iv)$ Thermal expansion