On heating a uniform metallic cylinder, its length increases by $3 \%$. The area of cross-section of its base will increase by ........... $\%$

Two large holes are cut in a metal sheet. If this sheet is heated,what happens to the distances $AB$ and $BC$ as shown in the figure?

Coefficient of linear expansion of brass and steel rods are $\alpha_1$ and $\alpha_2$. Lengths of brass and steel rods are $l_1$ and $l_2$ respectively. If $(l_2 - l_1)$ is maintained same at all temperatures,which one of the following relations holds good?

$A$ piece of metal has a weight of $49 \ gm$ in air and $39 \ gm$ in a liquid of density $1.2 \times 10^3 \ kg/m^3$ kept at $32^{\circ}C$. When the temperature of the liquid is raised to $42^{\circ}C$, the metal piece has a weight of $40 \ gm$. If the density of the liquid at $42^{\circ}C$ is $1.0 \times 10^3 \ kg/m^3$, then the coefficient of linear expansion of the metal is:

We would like to make a vessel whose volume does not change with temperature. We can use brass and iron $\left( {{\gamma _{{\text{brass}}}} = 6 \times {{10}^{ - 5}}/K} \right.$ and $\left. {{\gamma _{{\text{iron}}}} = 3.55 \times {{10}^{ - 5}}/K} \right)$ to create a volume of $100 \, cc$. How can you achieve this?

$A$ uniform rod of length $L$ pivoted at one end $P$ is freely rotated in a horizontal plane with an angular velocity $\omega$ about a vertical axis passing through $P$. If the temperature of the system is increased by $\Delta T$, the angular velocity becomes $\frac{\omega}{2}$. If the coefficient of linear expansion of the rod is $\alpha$ (where $\alpha \ll 1$), then $\Delta T$ will be: