$A$ body floats in water with $40 \%$ of its volume outside water. When the same body floats in an oil, $60 \%$ of its volume remains outside oil. The relative density of oil is

What is buoyancy?

$A$ heavy hollow cone of radius $R$ and height $h$ is placed on a horizontal table surface,with its flat base on the table. The whole volume inside the cone is filled with water of density $\rho$. The circular rim of the cone's base has a watertight seal with the table's surface and the top apex of the cone has a small hole. Neglecting atmospheric pressure,find the total upward force exerted by water on the cone.

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 $P_0$.)

Two bodies having volumes $V$ and $2V$ are suspended from the two arms of a common balance and they are found to balance each other. If the larger body is immersed in oil (density $d_1 = 0.9 \ gm/cm^3$) and the smaller body is immersed in an unknown liquid,the balance remains in equilibrium. The density of the unknown liquid is given by ......... $gm/cm^3$.

$A$ 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.