The length of a wire becomes l 1 and l 2 when 100 N and 120 N tension are applied respectively. If 10 l 2 = 11 l 1 , then the natural length of wire will be 1 x l 1 . Here the value of x is

Step-by-step solution

Young's modulus is given by Y = F A ∆ l l ⇒ F A = Y Δ l l ⇒ Δl = F l A Y ⇒ l + Δl = l 1 ⇒ F 1 L A Y + L = L F 1 A Y + 1 = l 1       . . . ( i ) Similarly, l 2 = F 2 A Y + 1 L ⇒ 10 l 2 = 11 l 1 It is given that 10 l 1 = 11 l 2 ⇒ 10 × L F 2 A Y + 1 = 11 L F 1 A Y + 1 ⇒ 10 F 2 A Y + 10 = 11 F 1 A Y + 11 Substituting F 1 = 100   N ,   F 2 = 120   N ⇒ 1200 A Y − 1100 A Y = 1 ⇒ 100 A Y = 1 ⇒ 1 A Y