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 l . Another wire of same material of length 2 L and radius 2 r is pulled by a force 2 f . Then the increase in its length will be:

Step-by-step solution

Young's modulus is same for both the wires since the material is same. For the first wire, Y = f L π r 2 l       . . . ( i ) For the second wire, Y = 2 f ( 2 L ) 4 π r 2 l '       . . . ( i i ) Dividing (i) by (ii) f L π r 2 l × 4 π r 2 l ' 4 f L = 1 ⇒ l ' = l