$A$ 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 $= 0.9$)

$A$ body having volume $V$ and density $\rho$ is attached to the bottom of a container as shown. The density of the liquid is $d$ (where $d > \rho$). The container has a constant upward acceleration $a$. The tension in the string is:

$A$ 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 $\,kg$)

Two cubical blocks identical in dimensions float in water in such a way that the $1$st block floats with half part immersed in water and the $2$nd block floats with $3/4$ of its volume inside the water. The ratio of densities of the blocks is ..........

$A$ metallic body of material with density of $8000\ kg/m^3$ has a cavity inside. $A$ spring balance shows its mass to be $10.0\ kg$ in air and $7.5\ kg$ when immersed in water. The ratio of the volume of the cavity to the volume of the material of the body must be

$A$ cone of radius $R$ and height $H$ is hanging inside a liquid of density $\rho$ by means of a string,as shown in the figure. The force due to the liquid acting on the slant surface of the cone is: