$A$ boat carrying a number of stones is floating in a water tank. If the stones are unloaded into the water,the water level in the tank will ............

$A$ cubical block of wood of specific gravity $0.5$ and a chunk of concrete of specific gravity $2.5$ are fastened together. The ratio of the mass of wood to the mass of concrete which makes the combination to float with its entire volume submerged under water is

Two pieces of metal when immersed in a liquid have equal upthrust on them; then

$A$ solid sphere of density $\rho_s$ which is $\eta$ $( > 1)$ times lighter than water (density $\rho_w$) is suspended in a water tank by a string tied to its base as shown in the figure. If the mass of the sphere is $m$,then the tension in the string is given by:

$A$ cube of ice floats partly in water and partly in kerosene oil. Find the ratio of the volume of ice immersed in water to that in kerosene oil. (Specific gravity of kerosene oil $= 0.8$, specific gravity of ice $= 0.9$)

$A$ 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: