Two solid pieces,one of steel and the other of aluminium,when immersed completely in water,have equal weights. When the solid pieces are weighed in air:

$A$ wooden block floats in a liquid with $40\%$ of its volume inside the liquid. When the vessel containing the liquid starts rising upwards with an acceleration $a = g/2$, the percentage of volume inside the liquid is ......... $\%$

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 $P_0$.)

$A$ container of liquid is in free fall. Without any liquid spilling out, does this container obey the principle of Archimedes?

$A$ 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:

$A$ weightless bag is filled with $5 \,kg$ of water and is weighed in water using a spring balance. The reading of the spring balance is (in $\,kg$)