A wooden cube just floats inside water with a $200 \,gm$ mass placed on it. When the mass is removed, the cube floats with its top surface $2 \,cm$ above the water level. the side of the cube is ......... $cm$
$6$
$8$
$10$
$12$
A wooden cube first floats inside water when a $200\,g$ mass is placed on it. When the mass is removed the cube is $2\,cm$ above water level. The side of cube is ........ $cm$
A vessel filled with water is kept on a weighing pan and the scale adjusted to zero. A block of mass $\mathrm{M}$ and density $\rho $ is suspended by a massless spring of spring constant $\mathrm{k}$. This block is submerged inside into the water in the vessel. What is the reading of the scale ?
A dumbbell is placed in water of density $\rho$ . It is observed that by attaching a mass $m$ to the rod, the dumbbell floats with the rod horizontal on the surface of water and each sphere exactly half submerged as shown in the figure. The volume of the mass $m$ is negligible. The value of length $l$ 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 slender homogeneous rod of length $2L$ floats partly immersed in water, being supported by a string fastened to one of its ends, as shown. The specific gravity of the rod is $0.75$. The length of rod that extends out of water is :