$A$ body weighs $50 \,g$ in air and $40 \,g$ in water. How much would it weigh in a liquid of specific gravity $1.5$ (in $\,g$)?

$A$ metallic sphere weighing $3 \,kg$ in air is held by a string so as to be completely immersed in a liquid of relative density $0.8$. The relative density of the metal is $10$. The tension in the string is ........ $N$.

$A$ sphere of radius $R$ made of a material of relative density $\sigma$ has a concentric cavity of radius $r$. It just floats when placed in a tank full of water. The value of the ratio $R/r$ will be:

$A$ wooden block of outer volume $1 \text{ litre}$ and specific gravity $\frac{3}{4}$ having a cavity floats with half of its volume immersed in water. Then the volume of the cavity is (in $\text{ ml}$)

$A$ body of density $d_1$ is counterpoised by $M$ of weights of density $d_2$ in air of density $d$. Then the true mass of the body is

$A$ cube of external side length $10 \ cm$ has an inner cubical cavity of side length $5 \ cm$. The density of the inner portion is twice that of the outer portion. If this cube is just floating in a liquid of density $2 \ g/cm^3$, find the density of the inner portion.