$A$ body floats in a liquid contained in a beaker. The whole system falls freely under gravity. The upthrust on the body due to the liquid is

$A$ body of density $\rho'$ is dropped from rest at a height $h$ into a lake of density $\rho$,where $\rho > \rho'$. Neglecting all dissipative forces,calculate the maximum depth to which the body sinks before returning to float on the surface.

$A$ cubical block of wood having a mass of $160 \,g$ has a metal piece fastened underneath as shown in the figure. Find the maximum mass of the metal piece which will allow the block to float in water. The specific gravity of wood is $0.8$, the specific gravity of the metal is $10$, and the density of water is $1 \,g/cm^3$. (in $\,g$)

The tension in a massless cable connected to an iron ball of $100 \,kg$ when it is submerged in sea water is (Given: $\rho_{\text{iron}} = 8 \times 10^3 \,kg/m^3$, $\rho_{\text{sea water}} = 1000 \,kg/m^3$, $g = 10 \,m/s^2$). (in $\,N$)

$A$ boat carrying a number of stones is floating in a water tank. If the stones are unloaded into the water,the water level in the tank will ............

$A$ $400 \ g$ solid cube having an edge of length $10 \ cm$ floats in water. How much volume of the cube is outside the water (in $cm^3$)? (Given: density of water $= 1000 \ kg/m^3$)