The figure shows a soap film in which a closed elastic thread is lying. The film inside the thread is pricked. Now the sliding wire is moved out so that the surface area increases. The radius circle of the circle formed by elastic thread will

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 in the thread. Surface tension of soap solution =0.030Nm^-1 .

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 in the thread. Surface tension of soap solution =0.030Nm^-1 .

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 in the thread. Surface tension of soap solution =0.030Nm^-1 .

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 in the thread. Surface tension of soap solution =0.030Nm^-1 .

A thin and light thread of sufficient length L is attached to a wire frame. The frame (along with the thread) is dipped into soap solution. When the frame is taken out of the solution, the thread takes the form of a semicircle with a soap film extending between the frame and the thread as shown in the figure ( a ). Now the thread is deformed into two semicircles by applying a force of F at the middle of the thread, as a result the film gets strectched as shown in the figure. ( b ). Calculate the surface tension of the soap solution.

A soap film is formed in a circular frame. A loop of thread of length 2 pi r is lying on the film. If the film inside the loop is broken then the tension in the thread will be

There are some experiment in which the outcomes cannot be identified discretely. For example, an ellipse of eccentricity 2sqrt(2)//3 is inscribed in a circle and a point within the circle is chosen at random. Now, we want to find the probability that this point lies outside the ellipse. Then, the point must lie in the shaded region shown in Figure. Let the radius of the circle be a and length of minor axis of the ellipse be 2b. Given that 1 - (b^(2))/(a^(2)) = (8)/(9) or (b^(2))/(a^(2)) = (1)/(9) Then, the area of circle serves as sample space and area of the shaded region represents the area for favorable cases. Then, required probability is p= ("Area of shaded region")/("Area of circle") =(pia^(2) - piab)/(pia^(2)) = 1 - (b)/(a) = 1 - (1)/(3) = (2)/(3) Now, answer the following questions. A point is selected at random inside a circle. The probability that the point is closer to the center of the circle than to its circumference is