$A$ block of steel of size $5 \times 5 \times 5 \, cm^3$ is weighed in water. If the relative density of steel is $7$,its apparent weight is ........... $g wt$.

$A$ ball of relative density $0.8$ falls into water from a height of $2 \ m$. The depth to which the ball will sink is ........ $m$ (neglect viscous forces):

$A$ cylindrical block of area of cross-section $A$ and of material of density $\rho$ is placed in a liquid of density one-third of the density of the block. The block compresses a spring,and the compression in the spring is one-third of the length of the block. If the acceleration due to gravity is $g$,the spring constant of the spring is:

$A$ 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 $\,m^3$)

$A$ 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:

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