String A B of unstretched length L is stretched by applying a force F at the mid-point C such that the segments A C and B C make an angle θ with A B as shown in the figure. The string may be considered as an elastic element with a force to elongation ratio K . The force F is given by

Step-by-step solution

Refer the diagram applying Lami's thorem, F sin 180 - 2 θ = T sin 90 + θ ∴     F sin 2 θ = T cos θ ⇒ F 2 sin θ cos θ = T cos θ ∴     F = 2 sin θ × T                 . . . 1 b u t   T = K × ∆ L = K × L 2 × 1 - cos θ cos θ put in equation 1 , F = 2 sin θ × K × L 2 × 1 - cos θ cos θ ∴       F = K L 1 - cos &