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

When the temperature of a body increases from $T$ to $T+\Delta T$,its moment of inertia increases from $I$ to $I+\Delta I$. If $\alpha$ is the coefficient of linear expansion of the material of the body,then $\frac{\Delta I}{I}$ is (neglect higher orders of $\alpha$ ).

On what value does the coefficient of linear expansion $\alpha_l$ depend? Write its unit.

Two different wires having lengths $L_{1}$ and $L_{2}$ and respective temperature coefficients of linear expansion $\alpha_{1}$ and $\alpha_{2}$ are joined end-to-end. Then the effective temperature coefficient of linear expansion is

$A$ bimetallic strip is formed out of two identical strips,one of copper and the other of brass. The coefficients of linear expansion of the two metals are $\alpha_C$ and $\alpha_B$. On heating,the temperature of the strip increases by $\Delta T$ and the strip bends to form an arc of radius $R$. Then $R$ is proportional to

Two rods $A$ and $B$ of identical dimensions are at temperature $30\,^{\circ}C$. If $A$ is heated up to $180\,^{\circ}C$ and $B$ up to $T\,^{\circ}C$,then the new lengths are the same. If the ratio of the coefficients of linear expansion of $A$ and $B$ is $4:3$,then the value of $T$ is........$^{\circ}C$.