In the figure shown,the heavy cylinder (radius $R$) resting on a smooth surface separates two liquids of densities $2\rho$ and $3\rho$. The height '$h$' for the equilibrium of the cylinder must be

$A$ thin vertical uniform wooden rod is pivoted at the top and immersed in water as shown. The container is slowly raised. At a certain moment,the equilibrium becomes unstable. If the density of water is $9/5$ times the density of wood,then the ratio of the total length of the rod to the submerged length of the rod at that moment is:

Given below are two statements:
$Statement$ $(I)$: Viscosity of gases is greater than that of liquids.
$Statement$ $(II)$: Surface tension of a liquid decreases due to the presence of insoluble impurities.
In the light of the above statements,choose the most appropriate answer from the options given below:

The volume of an air bubble becomes three times as it rises from the bottom of a lake to its surface. Assuming atmospheric pressure to be $75 \ cm$ of $Hg$ and the density of water to be $1/10$ of the density of mercury,the depth of the lake is ....... $m$.

Given below are two statements:
Statement $I$: When the speed of a liquid is zero everywhere,the pressure difference at any two points depends on the equation $P_1-P_2=\rho g(h_2-h_1)$.
Statement $II$: In the venturi tube shown,$2gh=v_2^2-v_1^2$.
In the light of the above statements,choose the most appropriate answer from the options given below.

Two blocks of ice when pressed together join to form one block because