A surveyor's $30$-$m$ steel tape is correct at some temperutre. 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 :-

A sphere of diameter $7\,\, cm$ and mass $266.5 \,\,gm$ floats in a bath of a liquid. As the temperature is raised, the sphere just begins to sink at a temperature $35^o C$. If the density of a liquid at $0^o C$ is $1.527 \,\,gm/cc$, then neglecting the expansion of the sphere, the coefficient of cubical expansion of the liquid is$f$ :

Water falls from a height $500m$. What is the rise in temperature of water at bottom if whole energy remains in the water ........... $^\circ \mathrm{C}$

A thin rod having a length of $1\; m$ and area of cross-section $3 \times 10^{-6}\,m ^2$ is suspended vertically from one end. The rod is cooled from $210^{\circ}\,C$ to $160^{\circ}\,C$. After cooling, a mass $M$ is attached at the lower end of the rod such that the length of rod again becomes $1\,m$. Young's modulus and coefficient of linear expansion of the rod are $2 \times 10^{11} Nm ^{-2}$ and $2 \times 10^{-5} K ^{-1}$, respectively. The value of $M$ is $.......kg .\left(\right.$ Take $\left.g=10\,m s ^{-2}\right)$

A pendulum clock (fitted with a small heavy bob that is connected with a metal rod) is $5\, seconds$ fast each day at a temperature of $15\,^oC$ and $10\,seconds$ slow at a temperature of $30\,^oC$. The temperature at which it is designed to give correct time, is ........ $^oC$

A non-isotropic solid metal cube has coefficients of linear expansion as:

$5 \times 10^{-5} /^{\circ} \mathrm{C}$ along the $\mathrm{x}$ -axis and $5 \times 10^{-6} /^{\circ} \mathrm{C}$ along the $y$ and the $z-$axis. If the coefficient of volume expansion of the solid is $\mathrm{C} \times 10^{-6} /^{\circ} \mathrm{C}$ then the value of $\mathrm{C}$ is