A rope of diameter 1 cm breaks when the tension applied exceeds 500 N . Determine the maximum tension that a similar rope with a diameter of 2 cm can withstand.

Step-by-step solution

Breaking stress is a property of the material and remains constant for similar ropes. Breaking stress is given by the ratio of breaking tension to the cross-sectional area: S = T A = 4T d^2 Since S is constant, the maximum tension T is directly proportional to the square of the diameter d : T d^2 Using the given values, we can write: T₂ T₁ = ( d₂ d₁ )^2 Substituting T₁ = 500 N , d₁ = 1 cm , and d₂ = 2 cm : T₂ 500 = ( 2 1 )^2 T₂ 500 = 4 T₂ = 2000 N