$A$ 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 $: 1$)

$A$ 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

$A$ block of steel of size $5 \text{ cm} \times 5 \text{ cm} \times 5 \text{ cm}$ is weighed in water. If the relative density of steel is $7$,its apparent weight is:

$A$ boat having a length of $3\,m$ and breadth $2\,m$ is floating on a lake. The boat sinks by $1\,cm$ when a man gets on it. The mass of the man is ....... $kg$. (Take density of water $\rho = 1000\,kg/m^3$ and $g = 10\,m/s^2$)

$A$ jar is filled with two non-mixing liquids $1$ and $2$ having densities $\rho_1$ and $\rho_2$ respectively. $A$ solid ball,made of a material of density $\rho_3$,is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for $\rho_1, \rho_2$ and $\rho_3$?

$A$ cube of ice floats partly in water and partly in kerosene oil. Find the ratio of the volume of ice immersed in water to that in kerosene oil. (Specific gravity of kerosene oil $= 0.8$, specific gravity of ice $= 0.9$)