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Question
A wire forming a loop is dipped into soap solution and taken out so that a film of soap solution is formed. A loop of 6.28 cm long thread is gently put on the film and the film is pricked with a needle inside the loop. The thread loop takes the shape of a circle. Find the tension the the thread. Surface tension of soap solution = 0.030 N m−1.
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Solution
The loop will take circular shape after pricking. Raduis of which is given by the relation.
Given:
Length of thread loop L = 6.28 cm
= 0.0628 m
Surface tension Ts = 0.030 N/m
Formula:
L = 2πr
r = `L/(2π)`
Solution:
`l = 2piR`
`R = l/(2pi)`
= `0.0628/ (2 xx 3.14)`
= `(0.0628)/ (6.28)`
= 0.01 m
= 10−2 m
∴ R = 10−2 m
2T sin dθ force in inward direction is balanced by the surface tension force in the outward direction.
∴ 2T sin(θ) = (surface tension ) × (length of are )
For small angles,
sin d(θ) = d(θ)
∴ 2Td(θ) = S(2Rdθ) ...(S = Surface tension)
∴ T = SR
= 10−2 × 0.030
= 3.0 × 10−4 N
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