$A$ body of density $1.2 \times 10^{3} \text{ kg/m}^3$ is dropped from rest from a height $1 \text{ m}$ into a liquid of density $2.4 \times 10^{3} \text{ kg/m}^3$. Neglecting all dissipative effects, the maximum depth to which the body sinks before returning to float on the surface is: (in $\text{ m}$)

Two cubes of size $1.0 \ m$ sides,one of relative density $0.60$ and another of relative density $1.15$ are connected by a weightless wire and placed in a large tank of water. Under equilibrium,the lighter cube will project above the water surface to a height of ........ $cm$.

$A$ 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:

$A$ cone of radius $R$ and height $H$ is hanging inside a liquid of density $\rho$ by means of a string,as shown in the figure. The force due to the liquid acting on the slant surface of the cone is:

$A$ boat carrying steel balls is floating on the surface of water in a tank. If the balls are thrown into the tank one by one,how will it affect the level of water?

$A$ boy carries a fish in one hand and a bucket (not full) of water in the other hand. If he places the fish in the bucket,the weight now carried by him (assume that water does not spill) is: