The moment of inertia $I$ of a uniform rod about a perpendicular bisector increases to $I+\Delta I$,if the temperature is increased slightly by $\Delta T$. If the coefficient of linear expansion is $\alpha$,then $\frac{\Delta I}{I}$ is (Assume $\frac{\Delta T}{T} \ll 1$)

$A$ metal ball initially at a pressure of $10^5 \ Pa$ is heated from $20^{\circ} C$ to $127^{\circ} C$ while keeping its volume constant. The coefficient of linear expansion of the metal is $10^{-5} \ {^{\circ} C}^{-1}$ and the bulk modulus of the metal is $2 \times 10^{11} \ N \ m^{-2}$. The final pressure inside the ball becomes:

The rods of length $L_1$ and $L_2$ are made of materials whose coefficients of linear expansion are $\alpha_1$ and $\alpha_2$ respectively. If the difference between the two lengths is independent of temperature,then:

$A$ 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 ..... $cm$.

Solids expand on heating because

The volume of the bulb of a mercury thermometer at $0^\circ C$ is $V_0$ and the cross-section of the capillary is $A_0$. The coefficient of linear expansion of glass is $a_g$ per $^\circ C$ and the coefficient of cubical expansion of mercury is $\gamma_m$ per $^\circ C$. If the mercury just fills the bulb at $0^\circ C$,what is the length of the mercury column in the capillary at $T^\circ C$?