NEET-XII-Physics
14: Some Mechanical Properties of Matter
- #29A 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.Ans : Given:
Surface tension of soap solution T = 0.030 N m-1
Let the radius of the thread loop be r.
`` \Rightarrow 2\,\mathrm{\,\pi \,}r=6.28\,\mathrm{\,cm\,}``
`` \Rightarrow r=\frac{6.28}{2\times 3.14}=1\,\mathrm{\,cm\,}``
The excess pressure inside the loop is expressed as follows:
`` ∆P=\frac{4T}{r}``
Tension in the thread:
`` T\text{'}=∆P\times \left(\,\mathrm{\,area\,}\,\mathrm{\,of\,}\,\mathrm{\,loop\,}\right)``
`` \Rightarrow T\text{'}=\frac{4T}{r}\times \,\mathrm{\,\pi \,}{r}^{2}``
`` \Rightarrow T\text{'}=4\,\mathrm{\,\pi \,}Tr``
`` =4\times 0.030\times 3.14\times {10}^{-2}\,\mathrm{\,N\,}``
`` =3.8\times {10}^{-3}\,\mathrm{\,N\,}``
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