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 solid metallic cube having total surface area $24\;m ^{2}$ is uniformly heated. If its temperature is increased by $10\,^{\circ} C$, calculate the increase in volume of the cube $\left(\right.$ Given $\left.: \alpha=5.0 \times 10^{-4}{ }^{\circ} C ^{-1}\right)$

A glass flask of volume one litre at $0^oC$ is filled, level full of mercury at this temperature. The flask and mercury are now heated to $100°C$ ........... $cc$ mercury will spill out, if coefficient of volume expansion of mercury is $1.82 \times {10^{ - 4}}°C^{-1}$ and linear expansion of glass is $0.1 \times {10^{ - 4}}°C^{-1}$ respectively

The coefficient of volumetric expansion of mercury is $18 × 10^{-5}{°C^{-1}}$. A thermometer bulb has a volume $10^{-6}\, m^3$ and cross section of stem is $ 0.004 \,cm^2$. Assuming that bulb is filled with mercury at $0°C$ then the length of the mercury column at $100°C$ is

A bar of iron is $10\, cm$ at $20°C$. At $19°C$ it will be ($\alpha$ of iron $= 11 \times 10^{-6}/°C$)

Two rods are joined between fixed supports as shown in the figure. Condition for no change in the lengths of individual rods with the increase of temperature will be

( ${\alpha _1},\,{\alpha _2},$ = linear expansion coefficient

$A_1, A_2$ = Area of rods

$Y_1, Y_2$ = Young modulus)