Two cylinders of same cross-section and length $L$ but made of two materials of densities $d_1$ and $d_2$ are cemented together to form a cylinder of length $2L$. The combination floats in a liquid of density $d$ with a length $L/2$ above the surface of the liquid. If $d_1 > d_2$,then:

An ice cube contains a large air bubble. The cube is floating on the horizontal surface of water contained in a trough. What will happen to the water level when the cube melts?

$A$ balloon of mass $m$ contains water of mass $M$. If it is completely immersed in water, find the apparent mass of the balloon with water in it.

$A$ 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

$A$ cube of edge length $10 \, cm$ is just balanced at the interface of two liquids $A$ and $B$ as shown in the figure. If liquids $A$ and $B$ have specific gravities $0.6$ and $0.4$ respectively,then the mass of the cube is ................ $g$.

$A$ ball of relative density $0.8$ falls into water from a height of $2 \ m$. The depth to which the ball will sink is ........ $m$ (neglect viscous forces):