Piece of ice floats in water at $4°\mathrm{C}$ kept in a beaker. When the ice melts completely, the water level in the beaker

A liquid of coefficient of volume expansion $\gamma$ fills a container of material having coefficient of linear expansion $\alpha$. If the liquid overflows on heating, then

The linear expansivity of glass is $\alpha$. Real expansivity of mercury is $\gamma$. The fraction of the whole volume of a glass vessel that has to be filled with mercury in order that the volume of the vessel not occupied by mercury may be the same at all temperatures is

The densities of a liquid at $0°\mathrm{C}$ and $100°\mathrm{C}$ are respectively $1.0127$ and $1$. A specific gravity bottle is filled with $300 \mathrm{g}$ of the liquid at $0°\mathrm{C}$ upto the brim and it is heated to $100°\mathrm{C}$. Then the mass of the liquid expelled in grams is (coefficient of linear expansion of glass$=9\times 10-6^{\circ }\mathrm{C}-1$)

A metal rod is fixed rigidly at two ends so as to prevent its thermal expansion. If $L$, $\alpha$ and $Y$ respectively denote the length of the rod, coefficient of linear thermal expansion and Young’s modulus of its material, then for an increase in temperature of the rod by $∆T$, the longitudinal stress developed in the rod is

Two non-reactive monoatomic ideal gases have their atomic masses in the ratio $2:3$. The ratio of their partial pressures, when inclosed in a vessel kept at a constant temperature, is $4:3$. The ratio of their densities is