$A$ man is sitting in a boat which is floating in a pond. If the man drinks some water from the pond,the level of water in the pond will

$A$ small metal sphere of density $\varrho$ is dropped from height $h$ into a jar containing liquid of density $\sigma$ $(\sigma > \varrho)$. The maximum depth up to which the sphere sinks is (Neglect damping forces).

$A$ solid cylinder of length $\ell$ and cross-sectional area $A$ is immersed such that it floats with its axis vertical at the liquid-liquid interface with length $\ell / 4$ in the denser liquid as shown in the figure. The lower density liquid has density $\varrho$ and the denser liquid has density $3\varrho$. The density $d$ of the solid cylinder is:

$A$ hemispherical portion of radius $R$ is removed from the bottom of a cylinder of radius $R$. The volume of the remaining cylinder is $V$ and its mass is $M$. It is suspended by a string in a liquid of density $\rho$ where it stays vertical. The upper surface of the cylinder is at a depth $h$ below the liquid surface. The force on the bottom of the liquid is

$A$ body of volume $V$ floats on water with $\frac{1}{3}$ of its volume above the surface. The volume of the object above the surface when floating on a liquid of specific gravity $1.5$ is

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 $\,N$)