A thin liquid film formed between a U-shaped wire and a light slider supports a weight of $1.5 \times 10^{-2}\mathrm{~N}$ (see figure). The length of the slider is 30 cm and its weight negligible. The surface tension of the liquid film is

JEE Main · 2012 · 29 Apr 2012 · Offline · Fluid Mechanics

A thin liquid film formed between a U-shaped wire and a light slider supports a weight of

1.5 \times 1 0^{- 2} N

(see figure). The length of the slider is 30 cm and its weight negligible. The surface tension of the liquid film is

(A) $0.0125 Nm^{- 1}$
(B) $0.1 Nm^{- 1}$
(C) $0.05 Nm^{- 1}$
(D) $0.025 Nm^{- 1}$ ✓ Correct

Answer: (D)

Solution

A liquid film has two surfaces, front and back, so the upward surface-tension force on the slider is

F = 2 T ℓ

, where

ℓ

is the slider's length. Balancing this against the weight it supports,

2 T ℓ = 1.5 \times 1 0^{- 2}

N with

ℓ = 0.30

m, gives

T = \frac{1.5 \times 1 0 ^{- 2}}{2 \times 0.30} = 2.5 \times 1 0^{- 2}

, that is

0.025 N m^{- 1}

JEE Main · 2012 · 29 Apr 2012 · Offline · Single correct option

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