$A$ 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 $= 19.3 \,g \,cm^{-3}$)

$A$ cube of side $40 \ cm$ is floating with $\frac{1}{4}$th of its volume immersed in water. When a circular disc is placed on the cube,it floats with $\frac{2}{5}$th of its volume immersed in water. The mass of the disc is (in $kg$)

$A$ hollow sphere of mass $M$ and radius $R$ is immersed in a tank of water (density $\rho_w$). The sphere would float if it were set free. The sphere is tied to the bottom of the tank by two wires which make an angle of $45^{\circ}$ with the horizontal as shown in the figure. The tension $T_1$ in each wire is:

$A$ hollow sphere of volume $V$ is floating on the water surface with half immersed in it. What should be the minimum volume of water poured inside the sphere so that the sphere now sinks into the water?

$A$ ball whose density is $0.4 \times 10^3 \, kg/m^3$ falls into water from a height of $9 \, cm$. To what depth does the ball sink? ....... $cm$

$A$ cubical block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with an acceleration of $g/3$, the fraction of volume immersed in the liquid will be