$A$ 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

$A$ man is carrying a block of a certain substance (of density $1000 \,kg/m^3$) weighing $1 \,kg$ in his left hand and a bucket filled with water and weighing $10 \,kg$ in his right hand. He drops the block into the bucket. How much load does he carry in his right hand now (in $,kg$)?

$A$ ball rises to the surface at a constant velocity in a liquid whose density is $3$ times greater than that of the material of the ball. The ratio of the force of friction acting on the rising ball to its weight is (in $: 1$)

$A$ solid sphere of radius $R$ and density $\rho$ is attached to one end of a massless spring of force constant $k$. The other end of the spring is connected to another solid sphere of radius $R$ and density $3\rho$. The complete arrangement is placed in a liquid of density $2\rho$ and is allowed to reach equilibrium. The correct statement$(s)$ is (are):
$(A)$ The net elongation of the spring is $\frac{4 \pi R^3 \rho g}{3 k}$
$(B)$ The net elongation of the spring is $\frac{8 \pi R^3 \rho g}{3 k}$
$(C)$ The light sphere is partially submerged.
$(D)$ The light sphere is completely submerged.

An iceberg floats in water with part of it submerged. What is the fraction of the volume of the iceberg submerged if the density of ice is ${\rho _i} = 0.917 \, g/cm^3$?

$A$ cubical block of density $\rho$ is floating on the surface of water. Out of its height $L$,a fraction $x$ is submerged in water. The vessel is in an elevator accelerating upward with acceleration $a$. What is the fraction immersed?