Two cubical blocks identical in dimensions float in water in such a way that $1$ st block floats with half part immersed in water and second block floats with $3 / 4$ of its volume inside the water. The ratio of densities of blocks is ..........
$2: 3$
$3: 4$
$1: 3$
$1: 4$
A uniform cylinder of length $L$ and mass $M$ having crosssectional area $A$ is suspended, with its length vertical, from a fixed point by a massless spring such that it is half submerged in a liquid of density $\sigma$ at equilibrium position. The extension $x_0$ of the spring when it is in equilibrium is
Four identical beakers contain same amount of water as shown below. Beaker $A$ contains only water. A lead ball is held submerged in the beaker $B$ by string from above. A same sized plastic ball, say a table tennis $(TT)$ ball, is held submerged in beaker $C$ by a string attached to a stand from outside. Beaker $D$ contains same sized $TT$ ball which is held submerged from a string attached to the bottom of the beaker. These beakers (without stand) are placed on weighing pans and register readings $w_{A}, w_{B}, w_{C}$ and $w_{D}$ for $A, B, C$ and $D$, respectively. Effects of the mass and volume of the stand and string are to be neglected.
A cubical block of wood $10 \,cm$ on a side floats at the interface between oil and water with its lower surface horizontal and $4\, cm$ below the interface. The density of oil is $0.6gc{m^{ - 3}}$. The mass of block is ...... $gm$
Write the only equation for the volume of partially immerged part of body float on the surface of liquid.
A sphere of relative density $\sigma$ and diameter $D$ has concentric cavity of diameter $d$. The ratio of $\frac{D}{d}$, if it just floats on water in a tank is: