$A$ metal ball of density $7800 \ kg/m^3$ is suspected to have a large number of cavities. It weighs $9.8 \ kg$ when weighed in air and $1.5 \ kg$ less when immersed in water. The fraction by volume of the cavities in the metal ball is approximately ....... $\%$

$A$ 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 . . . . . . $kg$.

What is buoyant force?

$A$ 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 $= 0.9$)

$A$ 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?

Determine the equation for the volume of the partially immersed part of a body floating in a fluid.