$A$ cubical block of steel of each side equal to $l$ is floating on mercury in a vessel. The densities of steel and mercury are $\rho_s$ and $\rho_m$. The height of the block above the mercury level is given by:

$A$ body is suspended by a light string. The tensions in the string when the body is in air,when the body is totally immersed in water,and when the body is totally immersed in a liquid are respectively $40.2 \,N$,$28.4 \,N$,and $16.6 \,N$. The density of the liquid is

At what depth does a body remain in equilibrium in a liquid? Explain.

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 ........ $cm$.

$A$ cube of wood supporting a $200 \, g$ mass just floats in water. When the mass is removed,the cube rises by $2 \, cm$. The side of the cube is ............ $cm$.

Two bodies having volumes $V$ and $2V$ are suspended from the two arms of a common balance and they are found to balance each other. If the larger body is immersed in oil (density $d_1 = 0.9 \ gm/cm^3$) and the smaller body is immersed in an unknown liquid,the balance remains in equilibrium. The density of the unknown liquid is given by ......... $gm/cm^3$.