Find the depth of a lake at which the density of water is $1\%$ greater than at the surface. Given the compressibility of water $K = 50 \times 10^{-6} \text{ atm}^{-1}$. (Take $1 \text{ atm} = 10^5 \text{ Pa}$) (in $\text{ km}$)

What is absolute pressure? And what is gauge pressure?

The Sun is a hot plasma (ionized matter) with its inner core at a temperature exceeding $10^{7} \; K$,and its outer surface at a temperature of about $6000 \; K$. At these high temperatures,no substance remains in a solid or liquid phase. In what range do you expect the mass density of the Sun to be,in the range of densities of solids and liquids or gases? Check if your guess is correct from the following data: mass of the Sun $= 2.0 \times 10^{30} \; kg$,radius of the Sun $= 7.0 \times 10^{8} \; m$.

Why do bags and suitcases have broad (wide) handles?

$A$ $U$ tube with both ends open to the atmosphere is partially filled with water. Oil,which is immiscible with water,is poured into one side until it stands at a distance of $10\, mm$ above the water level on the other side. Meanwhile,the water rises by $65\, mm$ from its original level (see diagram). The density of the oil is ......... $kg/m^3$.

Three identical vessels are filled with three liquids $A, B$, and $C$ with equal masses but having densities $\rho_A, \rho_B$, and $\rho_C$ respectively. If $\rho_A > \rho_B > \rho_C$, then the pressure at the bottom of the vessels will be: