A wire of length L and radius r is clamped at one end. If its other end is pulled by a force F , its length increases by l . If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become:

Step-by-step solution

The formula to calculate the Young's modulus of the material of the wire, in the first case, can be written as Y = F π r 2 l L . . . 1 From equation (1), it follows that F = Y π r 2 × l L . . . 2 For the second case, the Young's modulus is given by Y = F / 2 π r 2 / 4 l ' L . . . 3 From equation (3), it follows that F = Y l ' L × 2 × π r 2 4 . . . 4 From equations (2) and (4), it implies that Y π r 2 × l L = Y l ' L × 2 × π r 2 4 ⇒ l ' = 2 l