A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force F , its length increases by 5 cm . Another wire of the same material of length 4 L and radius 4 r is pulled by a force 4 F under same conditions. The increase in length of this wire is _____ cm .

Step-by-step solution

Young's modulus is given by Y = F L A ∆ L , here, A is cross-section area and ∆ L is change in length. Now, when force F is applied, change in length Δ L 1 = F L A Y = F L π r 2 Y = 5   cm Now, when force 4 F is applied, change in length Δ L 2 = 4   F 4 L π 16 r 2 Y = F L π r 2 Y = 5   cm