A hollow sphere of volume $V$ is floating on water surface with half immersed in it. What should be the minimum volume of water poured inside the sphere so that the sphere now sinks into the water

A cone of radius $R$ and height $H$, is hanging inside a liquid of density $\rho$ by means of a string as shown in the figure. The force, due to the liquid acting on the slant surface of the cone is

A solid cube and a solid sphere both made of same material are completely submerged in water but to different depths. The sphere and the cube have same surface area. The buoyant force is

A concrete sphere of radius $R$  has a cavity of radius $ r$  which is packed with sawdust. The specific gravities of concrete and sawdust are respectively $2.4$  and $0.3$  for this sphere to float with its entire volume submerged under water. Ratio of mass of concrete to mass of sawdust will be

A beaker containing water is placed on the platform of a spring balance. The balance reads $1.5$ $kg$. A stone of mass $0.5$ $kg$ and density $500$ $kg/m^3$ is immersed in water without touching the walls of beaker. What will be the balance reading now ? ….. $kg$