$A$ 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 ................ $g$.

$A$ metallic sphere weighing $3 \,kg$ in air is held by a string so as to be completely immersed in a liquid of relative density $0.8$. The relative density of the metal is $10$. The tension in the string is ........ $N$.

$A$ sphere of material of relative density $8$ has a concentric spherical cavity and just sinks in water. If the radius of the sphere is $2 \ cm$,then the volume of the cavity is

$A$ cubical block is floating in a liquid with one-fourth of its volume immersed in the liquid. If the whole system accelerates upward with an acceleration of $g / 4$,what will be the fraction of the volume immersed in the liquid?

$A$ solid cylinder of length $\ell$ and cross-sectional area $A$ is immersed such that it floats with its axis vertical at the liquid-liquid interface with length $\ell / 4$ in the denser liquid as shown in the figure. The lower density liquid has density $\varrho$ and the denser liquid has density $3\varrho$. The density $d$ of the solid cylinder is:

$A$ cubical block of side $0.5\,m$ floats on water with $30\%$ of its volume under water. What is the maximum weight (in $kg$) that can be put on the block without fully submerging it under water? [Take density of water $= 10^3\,kg/m^3$]