$A$ cubical block of wood having a mass of $160 \,g$ has a metal piece fastened underneath as shown in the figure. Find the maximum mass of the metal piece which will allow the block to float in water. The specific gravity of wood is $0.8$, the specific gravity of the metal is $10$, and the density of water is $1 \,g/cm^3$. (in $\,g$)

$A$ hollow spherical body of outer and inner radii of $4 \ cm$ and $2 \ cm$ respectively floats half submerged in a liquid of density $2.0 \ g \ cm^{-3}$. The density of the material of the sphere is (in $g \ cm^{-3}$)

$A$ homogeneous solid cylinder of length $L$ $(L < H/2)$, cross-sectional area $A$ is immersed such that it floats with its axis vertical at the liquid-liquid interface with length $L/4$ in the denser liquid (density $2d$) and $3L/4$ in the lighter liquid (density $d$). The lower density liquid is open to the atmosphere having pressure $P_0$. Then, the density $D$ of the solid is given by:

$A$ jar is filled with two non-mixing liquids $1$ and $2$ having densities $\rho_1$ and $\rho_2$ respectively. $A$ solid ball,made of a material of density $\rho_3$,is dropped in the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for $\rho_1, \rho_2$ and $\rho_3$?

If $W$ is the weight of a body of density $\rho$ in vacuum,then its apparent weight in air of density $\sigma$ is:

$A$ spring balance reads $200 \,gF$ when carrying a lump of lead in air. If the lead is now immersed with half of its volume in brine solution,what will be the new reading of the spring balance? The specific gravity of lead and brine are $11.4$ and $1.1$ respectively. (Result in $gF$)