Two brass rods $A$ and $B$ have lengths $l$ and $2l$ and radii $2r$ and $r$ respectively. If both are heated to the same temperature,the ratio of the increase in their volumes is:

The ratio of linear expansion coefficient,area expansion coefficient,and volume expansion coefficient is ...............

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 $T^\circ C$?

An iron tyre is to be fitted onto a wooden wheel $1 \, m$ in diameter. The diameter of the tyre is $6 \, mm$ smaller than that of the wheel. The tyre should be heated so that its temperature increases by a minimum of ........ $^oC$ (the coefficient of cubical expansion of iron is $3.6 \times 10^{-5} \, ^oC^{-1}$).

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 $\alpha$ ).

If the volume of a block of metal changes by $0.12 \%$ when heated through $20^{\circ} C$,then find its coefficient of linear expansion.