$A$ 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 $gF$)

As shown in the figure,a container is filled with a liquid of density $2d$ up to a height of $H/2$ and a liquid of density $d$ above it up to a height of $H/2$. $A$ solid cylinder of cross-sectional area $A/5$ and length $L$ $(L < H/2)$ is placed vertically in this container. The cylinder floats vertically such that its lower end is at a distance of $L/4$ from the interface of the two liquids. Find the density $D$ of the cylinder. (The atmospheric pressure at the surface of the upper liquid is $P_0$.)

$A$ $20 \,g$ copper block is suspended by a vertical spring causing $1 \,cm$ elongation over the natural length of the spring. If a beaker of water is placed below the block so that the copper block is completely immersed in the liquid, the elongation of the spring is (Density of copper = $9000 \,kg/m^3$, Density of water = $1000 \,kg/m^3$, $g = 10 \,m/s^2$) (in $\,cm$)

$A$ wooden block,with a coin placed on its top,floats in water as shown in the figure. The distances $l$ and $h$ are shown. After some time,the coin falls into the water. Then:

$A$ $400 \ g$ solid cube having an edge of length $10 \ cm$ floats in water. How much volume of the cube is outside the water (in $cm^3$)? (Given: density of water $= 1000 \ kg/m^3$)

$A$ wooden cube floats in water when a $200\,g$ mass is placed on it. When the mass is removed,the cube rises by $2\,cm$ above the water level. The side of the cube is ......... $cm$.