The reading of a spring balance when a block is suspended from it in air is $60\,N$. This reading changes to $40\,N$ when the block is immersed in water. The specific density (relative density) of the block is:

Two bodies placed on a balance are in equilibrium when immersed in water. If the mass of the first body is $36 \, g$ and its density is $9 \, g/cm^{3}$,and the mass of the second body is $48 \, g$,what is the density of the second body in $g/cm^{3}$?

$A$ gas in equilibrium has uniform density and pressure throughout its volume. This is strictly true only if there are no external influences. $A$ gas column under gravity,for example,does not have uniform density (and pressure). As you might expect,its density decreases with height. The precise dependence is given by the so-called law of atmospheres:
$n_{2}=n_{1} \exp \left[-m g\left(h_{2}-h_{1}\right) / k_{B} T\right]$
where $n_{2}, n_{1}$ refer to number density at heights $h_{2}$ and $h_{1}$ respectively. Use this relation to derive the equation for sedimentation equilibrium of a suspension in a liquid column:
$n_{2}=n_{1} \exp \left[-m g N_{A}\left(\rho-\rho^{\prime}\right)\left(h_{2}-h_{1}\right) /(\rho R T)\right]$
where $\rho$ is the density of the suspended particle,and $\rho^{\prime}$ that of the surrounding medium. [$N_{A}$ is Avogadro's number,and $R$ the universal gas constant.]

$A$ thin uniform cylindrical shell,closed at both ends,is partially filled with water. It is floating vertically in water in a half-submerged state. If $\rho_c$ is the relative density of the material of the shell with respect to water,then the correct statement is that the shell is

Find the apparent weight of a metallic block of density $5 \text{ g cm}^{-3}$ and dimensions $5 \text{ cm} \times 5 \text{ cm} \times 5 \text{ cm}$,in water.

Two cubical blocks identical in dimensions float in water in such a way that the $1$st block floats with half part immersed in water and the $2$nd block floats with $3/4$ of its volume inside the water. The ratio of densities of the blocks is ..........