A fluid container is containing a liquid of density $\rho $ is accelerating upward with acceleration a along the inclined place of inclination $\alpha$  as shown. Then the angle of inclination $ \theta $ of free surface 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 wooden block, with a coin placed on its top, floats in water as shown in fig. the distance $l $ and $h$ are shown there. After some time the coin falls into the water. Then

A ball whose density is $0.4 × 10^3 kg/m^3$ falls into water from a height of $9 cm$ . To what depth does the ball sink…….. $cm$

A cube of external dimension $10\  cm$ has an inner cubical portion of side $5\  cm$ whose density is twice that of the outer portion. If this cube is just floating in a liquid of density $2\  g/cm^3$, find the density of the inner portion