Gce Model Questions Vol1 2025 Further Mathematics Question 33

Practice objective / multiple choice question 33 from the 2025 Gce Model Questions Vol1 Further Mathematics examination.

Gce Model Questions Vol1 2025 Further Mathematics Objective / Multiple Choice Hard Difficulty
Question 33 GCE_MODEL_QUESTIONS_VOL1 • 2025 • FURTHER_MATHEMATICS • objective

A uniform beam \(AB\) of length \(6\text{ m}\) and weight \(1200\text{ N}\) is hinged at \(A\) to a vertical wall. The beam is supported by a cable attached at point \(C\) which is \(2\text{ m}\) from \(A\) along the beam and runs to a point \(D\) on the wall directly above \(A\). The cable makes an angle of \(30^{\circ}\) with the beam. A downward load of \(800\text{ N}\) is applied at \(B\). Determine (i) the tension in the cable, (ii) the horizontal and vertical components of the reaction at the hinge \(A\).

Answer Options

A. Tension \(T = 7200\text{ N}\). Reaction at A: \(R_{x}= -\frac{7200\sqrt{3}}{2}\text{ N}\) (≈‑6225 N), \(R_{y}= -2000\text{ N}\) (downward).
B. Tension \(T = 9000\text{ N}\). Reaction at A: \(R_{x}= -\frac{9000\sqrt{3}}{2}\text{ N}\) (≈‑7794 N), \(R_{y}= -2400\text{ N}\) (downward).
Correct Answer C. Tension \(T = 8400\text{ N}\). Reaction at A: \(R_{x}= -\frac{8400\sqrt{3}}{2}\text{ N}\) (≈‑7275 N), \(R_{y}= -2200\text{ N}\) (downward).
D. Tension \(T = 8400\text{ N}\). Reaction at A: \(R_{x}= -\frac{8400\sqrt{3}}{2}\text{ N}\) (≈‑7275 N), \(R_{y}= -2500\text{ N}\) (downward).
Correct Answer
C
Correct Option:
Tension \(T = 8400\text{ N}\). Reaction at A: \(R_{x}= -\frac{8400\sqrt{3}}{2}\text{ N}\) (≈‑7275 N), \(R_{y}= -2200\text{ N}\) (downward).

About This Question

This is Gce Model Questions Vol1 2025 Further Mathematics Question 33. It is one of the objective questions from the 2025 Gce Model Questions Vol1 Further Mathematics examination.

Difficulty level: Hard .

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