$A$ solid floats such that its $(1/3)$rd part is above the water surface. Then,the density of the solid is

$A$ hemispherical portion of radius $R$ is removed from the bottom of a cylinder of radius $R$. The volume of the remaining cylinder is $V$ and mass $M$. It is suspended by a string in a liquid of density $\rho$,where it stays vertical. The upper surface of the cylinder is at a depth $h$ below the liquid surface. The force on the bottom of the cylinder by the liquid is

State the law of floatation.

$A$ uniform cylinder of length $L$ and mass $M$ having cross-sectional area $A$ is suspended,with its length vertical,from a fixed point by a massless spring such that it is half submerged in a liquid of density $\sigma$ at equilibrium position. The extension $x_0$ of the spring when it is in equilibrium is

When an air bubble rises in water,does its potential energy increase or decrease?

The weight of a sphere in air is $50 \ g$. Its weight is $40 \ g$ in a liquid at temperature $20^{\circ} C$. When the temperature increases to $70^{\circ} C$,its weight becomes $45 \ g$. The ratio of the densities of the liquid at the two given temperatures is: (in $: 1$)