$A$ large ship can float but a steel needle sinks because of

$A$ 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.

$A$ $0.5\ kg$ mass of lead is submerged in a container filled to the brim with water and a block of wood floats on top. The lead mass is slowly lifted from the container by a thin wire and as it emerges into air the level of the water in the container drops a bit. The lead mass is now placed on the block of wood. As the lead is placed on the wood,what happens to the water level in the container?

$A$ body is suspended by a light string. The tensions in the string when the body is in air,when the body is totally immersed in water,and when the body is totally immersed in a liquid are respectively $40.2 \,N$,$28.4 \,N$,and $16.6 \,N$. The density of the liquid is

$A$ cubical block of wood with a side length of $10 \ cm$ floats at the interface between oil and water,with its lower surface horizontal and $4 \ cm$ below the interface. The density of oil is $0.6 \ g/cm^3$. The mass of the block is ......... $gm$.

$A$ 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 $\,g$)