JEE MainPhysicsMechanical Properties of Solids
A nylon rope of diameter 12 mm has a breaking strength of 3.6 10^4 N . What will be the breaking strength of a nylon rope of diameter 8 mm ?
Options
- A2.4 10^4 N
- B1.6 10^4 N
- C5.4 10^4 N
- D8.1 10^4 N
Correct answer
B. 1.6 10^4 N
Step-by-step solution
The breaking stress of a material is a constant property and does not depend on the dimensions of the rope. Breaking stress = Breaking strength (Force) Area of cross-section Let F₁ and F₂ be the breaking strengths of the ropes with diameters d₁ and d₂ respectively. F₁ d₁^2 4 = F₂ d₂^2 4 F₂ = F₁ ( d₂ d₁ )^2 Given F₁ = 3.6 10^4 N , d₁ = 12 mm , and d₂ = 8 mm : F₂ = 3.6 10^4 ( 8 12 )^2 F₂ = 3.6 10^4 ( 2 3 )^2 F₂ = 3.6 10^4 4 9 = 1.6 10^4 N Answer: 1.6 10^4 N