A wire in a circular shape has \(10 \Omega\) resistance. The resistance per one meter is \(1 \Omega\) The resultant between \(A \& B\) is equal to \(2.4 \Omega\), then the length of the chord \(\mathrm{AB}\) will be equal to (A) \(2.4\) (B) 4 (C) \(4.8\) (D) 6

The total resistance of the circular wire is 10Ω, and the resistance per meter is 1Ω. If we let the length of the wire be L, we can calculate the length of the wire by this formula: Total resistance = Resistance per meter * Length of wire 10Ω = 1Ω * L L = 10 meters Now, we know the length of the wire is 10 meters. Since the wire forms a circle, we have: Circumference = 2πr 10 = 2πr Divide both sides by 2π: r = 10 / 2π

Now that we have the radius of the circular wire, we can start finding the length of the chord AB which has a resistance of 2.4Ω between points A and B. Let's first find the length of the arc AB using the resistance formula: Resistance of AB = Resistance per meter * Length of arc AB 2.4Ω = 1Ω * Length of arc AB Length of arc AB = 2.4 meters Now, let's find the central angle θ formed by the arc AB (in radians): θ = (Length of arc AB) / r θ = 2.4/ (10 / 2π) θ = 0.48π Now that we have the central angle, we can find the length of the chord AB using the Law of Cosines. Considering a triangle formed by points O (center of the circle), A, and B: \(AB^2 = OA^2 + OB^2 - 2(OA)(OB)cos(θ)\) \(AB^2 = r^2 + r^2 - 2r^2 cos(0.48π)\) Plug in the value we obtained for r (10/2π meters) into the formula: \(AB^2 = (10 / 2π)^2 + (10 / 2π)^2 - 2(10 / 2π)^2 cos(0.48π)\) Calculate the value of AB²: \(AB^2 ≈ 4.8\) Now, obtain the value of AB by taking the square root: \(AB ≈ \sqrt{4.8}\) AB is approximately equal to 2.19 meters. Since 2.19 is not among the given options, the closest option is (A) 2.4.