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Surface Tension formula sheet

Every formula in the Surface Tension chapter for JEE Main, with one line on when it applies. Topic 1 is open to everyone; sign in free to read all 20 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 formula, and "last" is the latest year one appeared. ★ marks formulas asked 8 or more times.

Surface tension and surface energy

Surface tension
2× asked, last 2022
T=FL,Ffilm=2TLT=\frac FL,\qquad F_{\text{film}}=2TL
LL = contact line; a film has two surfaces. N/m = J/m2^2. 1 dyne/cm =10−3=10^{-3} N/m.
Ring lifted off; drop leaving a tube
Fring=4πRT,43πR3ρg=2πrTF_{\text{ring}}=4\pi RT,\qquad \tfrac43\pi R^3\rho g=2\pi rT
Ring: liquid touches both edges. Drop of radius RR falls from a tube of radius rr.
Drop floating half immersed
2× asked, last 2022
43πr3dg=23πr3ρg+2πrT,r=3T(2d−ρ)g\tfrac43\pi r^3dg=\tfrac23\pi r^3\rho g+2\pi rT,\qquad r=\sqrt{\frac{3T}{(2d-\rho)g}}
Drop density dd, liquid ρ\rho; buoyancy and surface tension both act up.
Work to enlarge a surface
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)
Isothermal. Soap bubble: two surfaces; liquid drop: one.
Splitting a drop into nn droplets
12× asked, last 2025
r=Rn1/3,W=4πR2T(n1/3−1)r=\frac R{n^{1/3}},\qquad W=4\pi R^2T(n^{1/3}-1)
Volume conserved; area becomes n1/3n^{1/3} times. 8 drops: 1 unit, 27: 2, 64: 3, 1000: 9.
Merging drops: energy released
4× asked, last 2025
ΔE=4πr2T(n−n2/3),ΔEV=3T(1r−1R)\Delta E=4\pi r^2T(n-n^{2/3}),\qquad \frac{\Delta E}V=3T\left(\frac1r-\frac1R\right)
nn drops of radius rr → one of R=n1/3rR=n^{1/3}r. Heating: Δθ=(3T/Jρs)(1/r−1/R)\Delta\theta=(3T/J\rho s)(1/r-1/R).
Temperature and impurities
3× asked, last 2025
T↓ as temperature↑T\downarrow\ \text{as temperature}\uparrow
Zero at the critical temperature. Soap, detergent, alcohol lower TT; salts (NaCl) raise it.

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13 more formulas in 3 topics

Excess pressure in drops and bubbles, Angle of contact and Capillarity. 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 pressure9×
  • Air bubble at a depth3×
  • Bubble inside a bubble2×
  • Two bubbles in contact2×
  • Bubbles merging isothermally1×

Angle of contact

  • Angle of contact5×

Capillarity

  • Capillary rise9×
  • Mass raised; energy
  • Inclined tube; tube in a lift1×
  • Tube shorter than the rise
  • U-tube with different bores1×
  • Rise between two parallel plates
  • Water film between two plates

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About 50 past JEE Main questions from this chapter, with instant answer checking and step-by-step solutions where available. Free, and you can start without signing up.

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