What is the change in volume of an iron sphere of volume $500 \,cm^3$, when it is heated from $0^{\circ} C$ to $100^{\circ} C$ (in $\,cm^3$)? (Given: $\alpha_{\text{Iron}} = 12 \times 10^{-6} /^{\circ} C$)

$A$ surveyor's $30$-$m$ steel tape is correct at some temperature. On a hot day,the tape has expanded to $30.01$ $m$. On that day,the tape indicates a distance of $15.52$ $m$ between two points. The true distance between these points is: (in $m$)

Three rods of length $\ell$ each are joined to form an equilateral triangle $PQR$. $O$ is the midpoint of $PQ$. For a small change in temperature,the distance $OR$ remains constant. If the coefficient of linear expansion for $PR$ and $RQ$ is $\alpha_2$ and for $PQ$ is $\alpha_1$,then:

$A$ composite rod made up of two rods $AB$ and $BC$ are joined at $B$. The rods are of equal length at room temperature and have equal masses. The coefficient of linear expansion $\alpha$ of $AB$ is more than that of $BC$. The composite rod is suspended horizontally by means of a thread at $B$. When the rod is heated:

The coefficient of volume expansion of a material is $5 \times 10^{-4} {^{\circ}C}^{-1}$. The fractional change in its density for a $40^{\circ}C$ rise in temperature is nearly.

$A$ $1$ litre glass flask contains some mercury. It is found that at different temperatures,the volume of air inside the flask remains the same. What is the volume of mercury in this flask in $cc$ if the coefficient of linear expansion of glass is $9 \times 10^{-6} /^{\circ}C$ and the coefficient of volume expansion of mercury is $1.8 \times 10^{-4} /^{\circ}C$?