$A$ boat carrying a number of stones is floating in a water tank. If the stones are unloaded into the water,the water level in the tank will ............

$A$ cubical block of density $\rho_{b} = 600 \ kg/m^3$ floats in a liquid of density $\rho_{l} = 900 \ kg/m^3$. If the height of the block is $H = 8.0 \ cm$, then the height of the submerged part is . . . . . . $cm$. (in $.3$)

$A$ metal ball of density $7800 \ kg/m^3$ is suspected to have a large number of cavities. It weighs $9.8 \ kg$ when weighed in air and $1.5 \ kg$ less when immersed in water. The fraction by volume of the cavities in the metal ball is approximately ....... $\%$

$A$ uniform rod is suspended horizontally from its mid-point. $A$ piece of metal whose weight is $w$ is suspended at a distance $l$ from the mid-point. Another weight $w_{1}$ is suspended on the other side at a distance $l_{1}$ from the mid-point to bring the rod to a horizontal position. When $w$ is completely immersed in water, $w_{1}$ needs to be kept at a distance $l_{2}$ from the mid-point to get the rod back into a horizontal position. The specific gravity of the metal piece is

An air bubble of radius $1\,cm$ in water has an upward acceleration of $9.8\,cm\,s^{-2}$. The density of water is $1\,g\,cm^{-3}$ and water offers negligible drag force on the bubble. The mass of the bubble is $.......g$.
$(g = 980\,cm\,s^{-2})$

The tension in a massless cable connected to an iron ball of $100 \,kg$ when it is submerged in sea water is (Given: $\rho_{\text{iron}} = 8 \times 10^3 \,kg/m^3$, $\rho_{\text{sea water}} = 1000 \,kg/m^3$, $g = 10 \,m/s^2$). (in $\,N$)