An elastic cord has an unstretched length of 30 cm . When subjected to a tension T , its length becomes 35 cm . When the tension is further increased by an amount T , the length of the cord becomes 50 cm . If T = xT , the value of x is _____.

Step-by-step solution

Let the force constant of the elastic cord be k . The unstretched length is L₀ = 30 cm . In the first case, the extension is x₁ = 35 - 30 = 5 cm . By Hooke's law, T = k(5) . In the second case, the total tension is T + T and the total extension is x₂ = 50 - 30 = 20 cm . So, T + T = k(20) . Dividing the two equations: T + T T = 20 5 = 4 1 + T T = 4 T = 3T Comparing with T = xT , we get x = 3 . Answer: 3