Engineering
Physics
Physical Quantities
SI Units
Stress Strain and Hookes Law New
Question
A rope 1 cm in diameter breaks if the tension in it exceeds 500 N. The maximum tension that may be given to a similar rope of diameter 2 cm is
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Solution
The breaking tension depends on the cross-sectional area, not diameter directly. Area A = πr² = π(d/2)² = (πd²)/4. Since the material is the same, maximum tension T is proportional to area, and thus to d².
Original rope: d₁ = 1 cm, T₁ = 500 N
New rope: d₂ = 2 cm
T₂ / T₁ = (d₂ / d₁)²
T₂ = T₁ × (d₂ / d₁)² = 500 N × (2/1)² = 500 N × 4
Final Answer: 2000 N