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📝 Hanging Cables And other Applications

📖 From Calculus • 7. Applications of the Definite Integral In Geometry, Science, and Engineering • 23 questions available

Practice MCQs for Hanging Cables And other Applications. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-16

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📝 Sample Questions

Q1. What is the equation of a uniform hanging cable (catenary) in terms of the parameter \(a\)?

🔹 A. \(y = a \sin\!\left(\frac{x}{a}\right)\)

🔹 B. \(y = a \cosh\!\left(\frac{x}{a}\right)\)

🔹 C. \(y = a e^{x/a}\)

🔹 D. \(y = a \tan\!\left(\frac{x}{a}\right\)

💡 Difficulty: easy | ✅ Correct: B

Q2. Two poles 20 m apart support a cable that sags 2 m at its midpoint. Which value of the catenary parameter \(a\) satisfies the sag relation \(s = a\bigl(\cosh(L/(2a)) - 1\bigr)\)?

🔹 A. \(a \approx 10\) m

🔹 B. \(a \approx 5\) m

🔹 C. \(a \approx 25\) m

🔹 D. \(a \approx 12\) m

💡 Difficulty: medium | ✅ Correct: C

Q3. A cable has linear density increasing with depth as \(\lambda(y)=\lambda_{0}(1+ky)\). Which integral gives its total weight?

🔹 A. \(W = g\displaystyle\int_{0}^{L}\lambda_{0}(1+ky)\,dy\)

🔹 B. \(W = g\displaystyle\int_{0}^{L}\lambda_{0}(1+ky)^{2}\,dy\)

🔹 C. \(W = \rho g\displaystyle\int_{0}^{L} y\,dA\)

🔹 D. \(W = \lambda_{0}g\,L\)

💡 Difficulty: hard | ✅ Correct: B

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🔗 Related Topics

📝 Approximating Roots 📝 Areas and Limits 📝 Continuity in Applications 📝 Continuity of Compositions 📝 Continuity of Inverse Functions

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