$A$ 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

$A$ rectangular block of size $10 \,cm \times 10 \,cm \times 15 \,cm$ is floating in water with the $10 \,cm$ side vertical. If it floats with the $15 \,cm$ side vertical,then the level of water will ..........

$A$ cube having a side of $10 \ cm$ with unknown mass $m$ and a $200 \ g$ mass were hung at two ends of a uniform rigid rod of $27 \ cm$ length. The rod along with the masses was placed on a wedge,keeping the distance between the wedge point and the $200 \ g$ weight as $25 \ cm$. Initially,the masses were not in balance. $A$ beaker is placed beneath the unknown mass and water is added slowly to it. At a given point,the masses were in balance and half the volume of the unknown mass was submerged in the water. (Take the density of the unknown mass to be greater than that of water,the mass did not absorb water,and the water density is $1 \ g/cm^3$). The unknown mass $m$ is . . . . . . $kg$.

$A$ dumbbell is placed in water of density $\rho$. It is observed that by attaching a mass $m$ to the rod,the dumbbell floats with the rod horizontal on the surface of water and each sphere exactly half submerged as shown in the figure. The volume of the mass $m$ is negligible. The value of length $l$ is

What is buoyant force?

$A$ 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 ............