$A$ body floats in water with $40 \%$ of its volume outside water. When the same body floats in oil, $60 \%$ of its volume remains outside oil. The relative density of the oil is

$A$ body of density $\rho$ is dropped from rest from a height $h$ into a lake of density $\sigma$,where $\sigma > \rho$. Neglecting all dissipative forces,the maximum depth to which the body sinks before returning to float on the surface is:

$A$ block of ice floats in an oil in a vessel. When the ice melts,the level of oil will ..............

$A$ solid sphere of density $\rho_s$ which is $\eta$ $( > 1)$ times lighter than water (density $\rho_w$) is suspended in a water tank by a string tied to its base as shown in the figure. If the mass of the sphere is $m$,then the tension in the string is given by:

$A$ wooden block of volume $1000\, cm^3$ is suspended from a spring balance. It weighs $12\, N$ in air. It is suspended in water such that half of the block is below the surface of water. The reading of the spring balance is ...... $N$.

Two non-mixing liquids of densities $\rho$ and $n\rho$ $(n > 1)$ are put in a container. The height of each liquid is $h$. $A$ solid cylinder of length $L$ and density $d$ is placed in this container. The cylinder floats with its axis vertical and a length $pL$ $(p < 1)$ submerged in the denser liquid. The density $d$ is equal to: