$A$ cubical block of wood with a side length of $10 \ cm$ floats at the interface between oil and water,with its lower surface horizontal and $4 \ cm$ below the interface. The density of oil is $0.6 \ g/cm^3$. The mass of the block is ......... $gm$.

An ice block contains a glass ball. When the ice melts within a vessel containing water,the level of the water

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

$A$ small solid ball is dropped from a height above the free surface of a liquid. It strikes the surface of the liquid at $t = 0$. The density of the material of the ball is $500 \ kg/m^3$ and that of the liquid is $1000 \ kg/m^3$. If the ball comes momentarily to rest at $t = 2 \ s$,then the initial height of the ball from the surface of the liquid was ..... $m$ (neglect viscosity).

$A$ 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:

$A$ block of iron contains a hollow cavity as shown below. The block weighs $6000 \,N$ in air and $4000 \,N$ in water. If the densities of iron and water are $6 \,g/cm^3$ and $1 \,g/cm^3$ respectively, then the volume of the cavity is (assume $g = 10 \,m/s^2$): (in $\,m^3$)