A glass flask of volume $200 \,cm ^3$ is just filled with mercury at $20^{\circ} C$. The amount of mercury that will overflow when the temperature of the system is raised to $100^{\circ} C$ is ........ $cm ^3$ $\left(\gamma_{\text {glase }}=1.2 \times 10^{-5} / C ^{\circ}, \gamma_{\text {mercury }}=1.8 \times 10^{-4} / C^{\circ}\right)$
$2.15$
$2.69$
$2.52$
$2.52$
A glass flask contains some mercury at room temperature. It is found that at different temperatures the volume of air inside the flask remains the same. If the volume of mercury in the flask is $300 \,\,cm^3$, then volume of the flask is ........ $cm^3$. (given that coefficient of volume expansion of mercury and coefficient of linear expansion of glass are $1.8 × 10^{-4} (^o C)^{-1}$ and $9 × 10^{-6} (^o C)^{-1}$ respectively)
Find out the increase in moment of inertia $I$ of a uniform rod (coefficient of linear expansion a) about its perpendicular bisector when its temperature is slightly increased by $\Delta T$.
A brass wire $1.8\; m$ long at $27\,^{\circ} C$ is held taut with little tension between two rigid supports. If the wire is cooled to a temperature of $-39\,^{\circ} C ,$ what is the tension developed in the wire, if its diameter is $2.0 \;mm$ ? Co-efficient of Itnear expansion of brass $=2.0 \times 10^{-5}\; K ^{-1} ;$ Young's modulus of brass $=0.91 \times 10^{11} \;Pa$
Surface of the lake is at $2°C$. Find the temperature of the bottom of the lake........ $^oC$
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: $\alpha_{steel} =1.20 \times 10^{-3} \;K ^{-1}$