The diameter of rain-drop is $0.02 \,cm$. If surface tension of water be $72 \times {10^{ - 3}}\,newton$ per metre, then the pressure difference of external and internal surfaces of the drop will be
$1.44 \times {10^4}\,dyne - c{m^{ - 2}}$
$1.44 \times {10^4}\,newton - {m^{ - 2}}$
$1.44 \times {10^3}\,dyne - c{m^{ - 2}}$
$1.44 \times {10^5}\,newton - {m^{ - 2}}$
A small soap bubble of radius $4\,cm$ is trapped inside another bubble of radius $6\,cm$ without any contact. Let $P_2$ be the pressure inside the inner bubble and $P_0$ the pressure outside the outer bubble. Radius of another bubble with pressure difference $P_2 - P_0$ between its inside and outside would be....... $cm$
When an air bubble of radius $r$ rises from the bottom to the surface of a lake, its radius becomes $\frac{{5r}}{4}$.Taking the atmospheric pressure to be equal to $10\,m$ height of water column, the depth of the lake would approximately be ....... $m$ (ignore the surface tension and the effect of temperature)
A spherical drop of water has radius $1\, mm$ If surface tension of water is $70 \times {10^{ - 3}}\,N/m$ difference of pressures between inside and out side of the spherical drop is ........ $N/{m^{ - 2}}$
Formation of bubble are in Column - $\mathrm{I}$ and pressure difference between them are given in Column - $\mathrm{II}$. Match them appropriately.
Column - $\mathrm{I}$ | Column - $\mathrm{II}$ |
$(a)$ Liquid drop in air | $(i)$ $\frac{{4T}}{R}$ |
$(b)$ Bubble of liquid in air | $(ii)$ $\frac{{2T}}{R}$ |
$(iii)$ $\frac{{2R}}{T}$ |
Two narrow bores of diameter $5.0\, {mm}$ and $8.0\, {mm}$ are joined together to form a $U-$shaped tube open at both ends. If this ${U}$-tube contains water, what is the difference in the level of two limbs of the tube.
[Take surface tension of water ${T}=7.3 \times 10^{-2} \, {Nm}^{-1}$, angle of contact $=0, {g}=10\, {ms}^{-2}$ and density of water $\left.=1.0 \times 10^{3} \,{kg} \,{m}^{-3}\right]$ (in $mm$)