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Surface Tension revision notes

Every idea in the Surface Tension chapter for JEE Main, with the usual mistakes and the fast methods. Topic 1 is open to everyone; sign in free to read all 18 and download the PDF.

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How we count: 7× asked means 7 past JEE Main questions in the PrepWiser bank needed that concept, and "last" is the latest year one appeared. ★ marks ideas asked 8 or more times.

Surface tension and surface energy

Surface tension as force per length
2× asked, last 2022
T=FL,Ffilm=2TLT = \frac{F}{L},\qquad F_{\text{film}} = 2TL
LL = length of the contact line. A film has two surfaces, so it pulls with 2TL2TL. Unit N/m = J/m².
F=2TLF=2TLLLfilm
The film pulls the slider in with 2TL2TL, one TLTL per surface
  • Ring of radius RR lifted off a liquid: the liquid touches both its inner and outer edge, so the extra pull is T(2πR+2πR)=4πRTT(2\pi R+2\pi R)=4\pi RT. A wire frame lifting a film needs 2TL2TL.
  • A drop of radius RR leaves a tube of radius rr when its weight beats the pull round the rim: (4/3)πR3ρg=2πrT(4/3)\pi R^3\rho g=2\pi rT.
Drop floating half immersed
2× asked, last 2022
43πr3d g=23πr3ρ g+2πrT,r=3T(2d−ρ) g\tfrac43\pi r^3 d\,g = \tfrac23\pi r^3\rho\,g + 2\pi r T,\qquad r=\sqrt{\frac{3T}{(2d-\rho)\,g}}
Drop density dd, liquid density ρ\rho. Surface tension acts upward along the waterline circle of length 2πr2\pi r.
  • Not (d−ρ)(d-\rho) or (d+ρ)(d+\rho). Only half the drop is submerged, so buoyancy uses half the volume, and buoyancy and surface tension both act upward against the weight.
Surface energy and work to enlarge a film
3× asked, last 2024
W=T ΔA,Wsoap bubble=8πT (r22−r12)W = T\,\Delta A,\qquad W_{\text{soap bubble}} = 8\pi T\,(r_2^2-r_1^2)
Slow, isothermal stretching. TT = surface energy per unit area. A soap bubble has area 2×4πr22\times4\pi r^2.
  • Not 4πT(r22−r12)4\pi T(r_2^2-r_1^2) for a soap bubble. Its film has an inner and an outer surface, so ΔA\Delta A doubles. A liquid drop has only one surface.
Splitting a drop into n droplets
12× asked, last 2025
r=Rn1/3,W=4πR2T (n1/3−1)r=\frac{R}{n^{1/3}},\qquad W = 4\pi R^2 T\,(n^{1/3}-1)
Volume is conserved. Total area becomes n1/3n^{1/3} times the original; WW = gain in surface energy.
  • Surface energy of nn small drops : one big drop =n1/3:1=n^{1/3}:1, whether the drops split or merge. Merging leaves 1/n1/31/n^{1/3} of the original surface energy; splitting multiplies it by n1/3n^{1/3}.
  • Not R=nrR=nr. Volume is conserved, so R=n1/3rR=n^{1/3}r and the big drop's area is n2/3n^{2/3} times one small drop's area, not nn times.
  • Quick method. Compare splits of the same drop by (n1/3−1)(n^{1/3}-1) alone: 8 drops give 1 unit, 27 give 2, 64 give 3, 1000 give 9. JEE picks perfect cubes so n1/3n^{1/3} is a whole number.
Merging drops: energy released and heating
4× asked, last 2025
ΔE=4πr2T (n−n2/3),ΔEV=3T(1r−1R)\Delta E = 4\pi r^2 T\,(n-n^{2/3}),\qquad \frac{\Delta E}{V}=3T\left(\frac1r-\frac1R\right)
nn drops of radius rr form one drop of radius R=n1/3rR=n^{1/3}r. The released energy heats the liquid.
  • All released energy goes into heat: Δθ=(3T/Jρs)(1/r−1/R)\Delta\theta=(3T/J\rho s)(1/r-1/R), with ss = specific heat and JJ to turn joules into calories. Splitting a drop cools it the same way.
Effect of temperature and impurities
3× asked, last 2025
  • TT falls as temperature rises and becomes zero at the critical temperature. So the same capillary holds a shorter column of hot water than of cold water.
  • Not higher TT for soap water. Soap and detergents lower the surface tension of water, which is how they wet and clean. Dissolved salts such as NaCl raise it; alcohol lowers it.
Also remember
  • Not mixed units: 11 dyne/cm =10−3=10^{-3} N/m, 11 N/cm =100=100 N/m, 11 erg =10−7=10^{-7} J. Convert to SI first; many wrong options are exactly a power of ten off.

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Practise Surface Tension

12 more concepts in 4 topics

Excess pressure in drops and bubbles, Angle of contact and Capillarity, plus ideas from measurement and flow. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Excess pressure in drops and bubbles

  • Excess pressure across a curved surface9×
  • Air bubble at a depth3×
  • Bubble inside a bubble2×
  • Two bubbles in contact2×
  • Bubbles merging isothermally1×

Angle of contact

  • Angle of contact5×
  • Also remember1

Capillarity

  • Capillary rise9×
  • Inclined capillary and capillary in a lift1×
  • Tube shorter than the capillary rise
  • U-tube with bores of different radii1×
  • Rise between two parallel plates
  • Water film between two plates

Also asked here: measurement and flow

  • Key points2

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