$A$ hollow sphere of external radius $R$ and thickness $t$ $(t \ll R)$ is made of a metal of density $\rho$. The sphere will float in water if:

$A$ wooden block is floating on water kept in a beaker. $40 \%$ of the block is above the water surface. Now the beaker is kept inside a lift that starts going upward with acceleration equal to $g / 2$. The block will then

The diagram shows a jar filled with two non-mixing liquids $1$ and $2$ having densities ${\rho _1}$ and ${\rho _2}$ respectively. $A$ solid ball,made of a material of density ${\rho _3}$,is dropped into the jar. It comes to equilibrium in the position shown in the figure. Which of the following is true for ${\rho _1}$,${\rho _2}$ and ${\rho _3}$?

$A$ hollow spherical shell of outer radius $R$ floats just submerged under the water surface. The inner radius of the shell is $r$. If the specific gravity of the shell material is $\frac{27}{8}$ with respect to water,the value of $r$ is $......R$.

$Assertion$ : $A$ balloon filled with hydrogen will fall with acceleration $\frac{g}{6}$ on the moon.
$Reason$ : Moon has no atmosphere.

An iceberg floats in sea water with a part of it submerged. The percentage fraction of the iceberg which is unsubmerged is (Density of ice $= 0.9 \text{ g/cm}^3$, density of sea water $= 1.1 \text{ g/cm}^3$). (in $\%$)