$A$ 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 ........ $N$.

$A$ block of ice floats on a liquid of density $1.2 \ g/cm^3$ in a beaker. What happens to the level of the liquid when the ice completely melts?

$A$ piece of gold weighs $10 \,g$ in air and $9 \,g$ in water. What is the volume of the cavity in $cc$? (Density of gold $= 19.3 \,g \,cm^{-3}$)

The ratio of masses of a cubical block of wood and a chunk of concrete is $\frac{3}{5}$ so that the combination just floats with its entire volume submerged under water. If the specific gravity of wood is $0.5$,then the specific gravity of concrete will be:

An object suspended by a wire stretches it by $10 \,mm$. When the object is immersed in a liquid,the elongation in the wire reduces by $\frac{10}{3} \,mm$. The ratio of the relative densities of the object and the liquid is ............

$A$ 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