A wire forming a loop is submerged into a soap solution and removed, establishing a film of soap solution. A loop of thread 6.28 cm long is gently placed on the film, and the film is subsequently pricked with a needle inside the loop. The thread loop assumes a circular shape. Determine the tension in the thread. The surface tension of the soap solution is 0.030 N/m .

Step-by-step solution

The length of the thread loop is given by L = 2 R = 6.28 cm = 6.28 10⁻² m . The radius of the circular loop is R = 6.28 10⁻² 2 3.14 = 10⁻² m . When the film inside the loop is pricked, the outer soap film pulls the thread radially outward. Since a soap film has two free surfaces, the outward force per unit length is 2S , where S is the surface tension. Considering a small element of the thread subtending an angle d at the center, the outward force on this element is dF = (2S)(R d ) . This outward force is balanced