What will happen if a rod is tied with fixed supports rigidly at both ends and its temperature is increased?

The length of a metal rod at $30^{\circ} C$ is $30 \ cm$. If its temperature is raised to $105^{\circ} C$, its length is increased by $0.027 \ cm$. Then the coefficient of linear expansion of the metal is

At some temperature $T$,a bronze pin is slightly too large to fit into a hole drilled in a steel block. The change in temperature required for an exact fit is minimum when:

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

Two rods,one of aluminum and another of steel,have initial lengths $l_1$ and $l_2$ respectively. They are joined together to form a single rod of length $(l_1 + l_2)$. If the coefficients of linear expansion for aluminum and steel are $\alpha_a$ and $\alpha_s$ respectively,and the increase in length for both rods is the same when the temperature of both is increased by $t \ ^\circ C$,then $\frac{l_1}{l_1 + l_2} = \dots$

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 $\%$)