Two persons are pulling a rope towards themselves. Each person applies a force of 100 N on the rope. Determine the Young modulus of the rope's material if it extends in length by 1 cm . The original length of the rope is 2 m and its cross-sectional area is 2 cm ^2 .

Step-by-step solution

Since two persons are pulling the rope from opposite ends with a force of 100 N each, the tension developed in the rope is F = 100 N . The given parameters are L = 2 m , L = 1 cm = 10⁻² m , and A = 2 cm ^2 = 2 10⁻⁴ m ^2 . The Young modulus is given by Y = F L A L . Substituting the values: Y = 100 2 2 10⁻⁴ 10⁻² Y = 200 2 10⁻⁶ Y = 1 10^8 N/m ^2