$A$ sphere of material of relative density $8$ has a concentric spherical cavity and just sinks in water. If the radius of the sphere is $2 \ cm$,then the volume of the cavity is

$A$ spring balance $A$ reads $2 \,kg$ with a block of mass $m$ suspended from it. Another balance $B$ reads $3 \,kg$ when a beaker with a liquid is put on its pan. The two balances are now so arranged that the hanging mass $m$ is fully immersed inside the liquid in the beaker as shown in the figure. In this situation,

$A$ cubical block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with a net acceleration of $g/3$,the fraction of volume immersed in the liquid will be:

When an air bubble rises in water,does its potential energy increase or decrease?

The fraction of a floating object of volume $V_0$ and density $d_0$ above the surface of a liquid of density $d$ will be

$A$ cube of side $40 \ cm$ is floating with $\frac{1}{4}$th of its volume immersed in water. When a circular disc is placed on the cube,it floats with $\frac{2}{5}$th of its volume immersed in water. The mass of the disc is (in $kg$)