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?

$A$ cylinder has a piston at a temperature of $30^{\circ} C$. There is an all-round clearance of $0.08 \ mm$ between the piston and the cylinder wall. If the internal diameter of the cylinder is $15 \ cm$,what is the temperature at which the piston will fit into the cylinder exactly (in $^{\circ} C$)? $(\alpha_p = 1.6 \times 10^{-5} /^{\circ} C$ and $\alpha_c = 1.2 \times 10^{-5} /^{\circ} C)$

$A$ steel scale measures the length of a copper wire as $80.0\,cm$ when both are at $20^\circ C$ (the calibration temperature for the scale). What would be the scale reading for the length of the wire when both are at $40^\circ C$ (in $,cm$)?

$A$ solid metal sphere has a spherical cavity inside it. If the sphere is heated,the volume of the cavity will.....

Three uniform thin aluminium rods each of length $2 \,m$ form an equilateral triangle $PQR$ as shown in the figure. The midpoint of the rod $PQ$ is at the origin of the coordinate system. If the temperature of the system of rods increases by $50^{\circ} C$, the increase in $y$-coordinate of the centre of mass of the system of the rods is ............ $mm$. (Coefficient of volume expansion of aluminium $= 12 \sqrt{3} \times 10^{-6} \,K^{-1}$)

When a body is heated, then the maximum rise will be in its