$A$ hollow sphere of external radius $R$ and thickness $t$ $(t \ll R)$ is made of a metal of density $\rho$. The sphere will float in water if:

$A$ concrete sphere of radius $R$ has a cavity of radius $r$ which is packed with sawdust. The specific gravities of concrete and sawdust are $2.4$ and $0.3$ respectively. For this sphere to float with its entire volume submerged under water,the ratio of the mass of concrete to the mass of sawdust will be:

$A$ ball whose density is $0.4 \times 10^3 \ kg/m^3$ falls into water from a height of $9 \ cm$. To what depth does the ball sink in $cm$?

$A$ metal cube is embedded inside a block of ice that is floating on the surface of water. The ice melts completely, and the metal cube sinks into the water. What happens to the water level in the container?

$A$ sample of metal weighs $210 \ g$ in air,$180 \ g$ in water,and $120 \ g$ in a liquid. Then,the relative density $(RD)$ of:

$A$ container of large surface area is filled with a liquid of density $\rho$. $A$ cubical block of side edge $a$ and mass $M$ is floating in it with four-fifths of its volume submerged. If a coin of mass $m$ is placed gently on the top surface of the block,it is just submerged. $M$ is: