A force F applied on the wire of radius r and length L and change in the length of the wire is l. If the same force F is applied on the wire of the same material and radius 4 r and length 4 l , then change in length of the other wire is,

Step-by-step solution

Young's modulus Y is defined as Y = F L A l , where A = r^2 is the cross-sectional area of the wire. For the first wire, Y = F L ( r^2) l . For the second wire, let the change in length be l' . The material is the same, so Y remains constant. The force is F , the radius is 4r , and the length is 4L . Y = F (4L) (4r)^2 l' = 4 F L 16 r^2 l' = F L 4 r^2 l' . Equating the expressions for Y : F L r^2 l = F L 4 r^2 l' 1 l = 1 4 l' l' = l 4 . Answer: l 4