$A$ ball whose density is $0.4 \times 10^3 \, kg/m^3$ falls into water from a height of $9 \, cm$. To what depth does the ball sink? ....... $cm$

$A$ cube of external side length $10 \ cm$ has an inner cubical cavity of side length $5 \ cm$. The density of the inner portion is twice that of the outer portion. If this cube is just floating in a liquid of density $2 \ g/cm^3$, find the density of the inner portion.

An empty balloon weighs $1\, g$. The balloon is filled with water to the neck and tied with a massless thread. The weight of the balloon along with water is $101\, g$. The balloon filled with water is weighed when fully immersed in water. Its weight in water is ...... $g$.

As shown in the figure,a container is filled with a liquid of density $2d$ up to a height of $H/2$ and a liquid of density $d$ above it up to a height of $H/2$. $A$ solid cylinder of cross-sectional area $A/5$ and length $L$ $(L < H/2)$ is placed vertically in this container. The cylinder floats vertically such that its lower end is at a distance of $L/4$ from the interface of the two liquids. Find the density $D$ of the cylinder. (The atmospheric pressure at the surface of the upper liquid is $P_0$.)

Why is it easier to swim in sea water than in river water?

$A$ $20 \,g$ copper block is suspended by a vertical spring causing $1 \,cm$ elongation over the natural length of the spring. If a beaker of water is placed below the block so that the copper block is completely immersed in the liquid, the elongation of the spring is (Density of copper = $9000 \,kg/m^3$, Density of water = $1000 \,kg/m^3$, $g = 10 \,m/s^2$) (in $\,cm$)