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

A solid ball is completely immersed in a liquid. The coefficients of volume expansion of the ball and liquid are $3 × 10^{-6}$ and $8 × 10^{-6} per ^o C$ respectively. The percentage change in upthrust when the temperature is increased by $100 ^o C$ is ....... $\%$

What will happen if a rod is tied with fixed supports rigidly at both ends and temperature is increased ?

A rod of length $10\ meter$ at $0\,^oC$ having expansion coefficient $\alpha  = (2x^2 + 1) \times  10^{-6}\,C^{-1}$ where $x$ is the distance from one end of rod. The length of rod at $10\,^oC$ is

A large steel wheel is to be fitted on to a shaft of the same material. At $27\,^{\circ} C ,$ the outer diameter of the shaft is $8.70\; cm$ and the diameter of the centrall hole in the wheel is $8.69 \;cm$. The shaft is cooled using 'dry ice'. At what temperature (in $^oC$) of the shaft does the wheel slip on the shaft? Assume coefficient of linear expansion of the steel to be constant over the required temperature range: $\alpha_{steel} =1.20 \times 10^{-3} \;K ^{-1}$

Consider two thermometers $T_1$ and $T_2$ of equal length, which can be used to measure temperature over the range $\theta_1$ to $\theta_2$. $T_1$ contains mercury as the thermometric liquid, while $T_2$ contains bromine. The volumes of the two liquids are the same at the temperature $\theta_1$. The volumetric coefficients of expansion of mercury and bromine are $18 \times 10^{-5} \,K ^{-1}$ and $108 \times 10^{-5} \,K ^{-1}$, respectively. The increase in length of each liquid is the same for the same increase in temperature. If the diameters of the capillary tubes of the two thermometers are $d_1$ and $d_2$, respectively. Then, the ratio of $d_1: d_2$ would be closest to