Bernoulli S Principle

The increase in the length of a wire under an applied force is given by the formula: where: - is the applied force, - is the original length of the wire, - is the cross-sectional area of the wire, and - is Young's modulus of the material. Since the wires are made of the same material, the value of is the same for both wires. Also, the applied force is the same for both wires. Therefore, the increase in length is proportional to the ratio . The cross-sectional area of a wire with diameter is given by: Let the diameter of wire A be and the diameter of wire B be . Since , we can write: Now, the increase in length for wire A and wire B will be: Given that and , we get: Thus, the ratio of the increase in lengths of wires A and B is .