$A$ block of iron contains a hollow cavity as shown below. The block weighs $6000 \,N$ in air and $4000 \,N$ in water. If the densities of iron and water are $6 \,g/cm^3$ and $1 \,g/cm^3$ respectively, then the volume of the cavity is (assume $g = 10 \,m/s^2$): (in $\,m^3$)

$A$ cube of edge length $10 \, cm$ is just balanced at the interface of two liquids $A$ and $B$ as shown in the figure. If liquids $A$ and $B$ have specific gravities $0.6$ and $0.4$ respectively,then the mass of the cube is ................ $g$.

$A$ 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 $\text{ ml}$)

$A$ cylindrical block of wood of base area $30 \, cm^2$ floats in a liquid of density $900 \, kg/m^3$. The block is depressed lightly and then released. The time period of the resulting oscillations of the block is equal to that of a spring with a block of the same mass. The spring constant is equal to ........ $N/m$.

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

$A$ wax candle floats vertically in a liquid of density twice that of wax. The candle burns at the rate of $4\ cm/hr$. Then, with respect to the surface of the liquid, the upper end of the candle will: