The relative density of Kerosene is $0.8$. Find its density. (in $kg/m^3$)

When an air bubble of radius $r$ rises from the bottom to the surface of a lake,its radius becomes $\frac{5r}{4}$. If the atmospheric pressure is equal to the pressure exerted by a $10 \ m$ height of water column,the temperature is constant,and surface tension is neglected,what is the depth of the lake (in $m$)?

Liquid is ...... while gas is ...... . (Fill in the blank) [incompressible,compressible]

Fill in the blanks:
$(i)$ $1 \text{ atm} = \dots \text{ Pascal}$
$(ii)$ $1 \text{ torr} = \dots \text{ Pascal}$
$(iii)$ $1 \text{ bar} = \dots \text{ Pa}$
$(iv)$ $1 \text{ atm} = \dots \text{ cm Hg}$

Three identical vessels are filled to the same height with three different liquids $A, B$ and $C$ $(\rho_A > \rho_B > \rho_C)$. The pressure at the base will be

$A$ spherical marble of radius $1 \, cm$ is stuck in a circular hole of radius slightly smaller than its own radius (for calculation purpose,both can be taken same) at the bottom of a bucket filled with water up to a height of $10 \, cm$. If the mass of the marble is $20 \, g$,then the net force on the marble due to water is close to: