$A$ glass flask weighing $390 \ g$,having an internal volume of $500 \ cm^3$,just floats when half of it is filled with water. The specific gravity of the glass is:

$A$ 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

$A$ wide-bottomed cylindrical massless plastic container of height $9 \, cm$ contains $40$ identical coins and is floating on water with $3 \, cm$ of its height submerged. If we start placing additional identical coins on its lid,it is observed that after $N$ coins are added,the equilibrium changes from stable to unstable. Equilibrium in floating is stable if the geometric centre of the submerged portion is above the centre of mass of the object. The value of $N$ is closest to:

$A$ vessel contains oil (density = $0.8 \text{ g/cm}^3$) over mercury (density = $13.6 \text{ g/cm}^3$). $A$ homogeneous sphere floats with half of its volume immersed in mercury and the other half in oil. The density of the material of the sphere in $\text{g/cm}^3$ is

$A$ wooden block floats in a liquid with $40\%$ of its volume inside the liquid. When the vessel containing the liquid starts rising upwards with an acceleration $a = g/2$, the percentage of volume inside the liquid is ......... $\%$

$A$ rectangular block is $5 \ cm \times 5 \ cm \times 10 \ cm$ in size. The block is floating in water with the $5 \ cm$ side vertical. If it floats with the $10 \ cm$ side vertical,what change will occur in the level of water?