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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.
Solution
The loop will take circular shape after pricking. Raduis of which is given by the relation.
`l = 2 (pi) R or R = 1/(2pi) = 6.28 / (2 xx 3.14) = 1 cm`
=10-2 m
2T sin dθ force in inward direction is balanced by surface tension force in out ward dirction.
∴ 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
=(0.020) (10-2 )
= 3.0 × 10-4 N.
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