$A$ body is just floating on the surface of a liquid. The density of the body is the same as that of the liquid. The body is slightly pushed down. What will happen to the body?

$A$ 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

$A$ wooden cube of side $10 \ cm$ floats at the interface between water and oil with its lower surface $3 \ cm$ below the interface. If the density of oil is $0.9 \ g \ cm^{-3}$,the mass of the wooden cube is (in $g$)

$A$ 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

$A$ uniform rod of density $\rho$ is placed in a wide tank containing a liquid of density $\rho_0$ $(\rho_0 > \rho)$. The depth of the liquid in the tank is half the length of the rod. The rod is in equilibrium,with its lower end resting on the bottom of the tank. In this position,the rod makes an angle $\theta$ with the horizontal.

$A$ 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 its mass is $M$. 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 liquid is