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Question

A massless inextensible string in the form of a loop is placed on a horizontal film of soap solution of surface tension T. If film is pierced inside the loop and it convert into a circular loop of diameter d, then the tension produced in string is :

A
Td
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B
πTd
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C
πd2T
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D
πd2T4
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Solution

The correct option is A Td
T(surface tension)
d-diameter of loop
At equillibrium
2TΔl=2Fsinθ2
since θ is very small so sinθ2θ2
TΔl=Fθ/2
Δl=rθ=dθ2
so, T×dθ2=F×θ2
F=Td.

1446549_1156336_ans_9dc9067af78c485493c1133271e95f77.png

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