A piece of copper having an internal cavity weights $264\, g$ in air and $221\, g$ in water. Find volume (in $cc$) of cavity. Density of $Cu = 8.8\, g/cc$

A fluid container is containing a liquid of density $\rho $ is accelerating upward with acceleration a along the inclined place of inclination $\alpha$  as shown. Then the angle of inclination $ \theta $ of free surface is :

A boat having some iron pieces is floating in a pond. If iron pieces are thrown in the liquid then level of liquid

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 cylinder is at a depth $h$ below the liquid surface. The force on the bottom of the cylinder by the liquid is

A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating vertically in water in half-submerged state. If $\rho_0$ is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is

In Guericke's experiment to show the effect of atmospheric pressure, two copper hemispheres were tightly fitted to each other to form a hollow sphere and the air from the sphere was pumped out to create vacuum inside. If the radius of each hemisphere is $R$ and the atmospheric pressure is $p$, then the minimum force required (when the two hemispheres are pulled apart by the same force) to separate the hemispheres is