Gce Model Questions Vol1 2024 Further Mathematics Question 42

Practice objective / multiple choice question 42 from the 2024 Gce Model Questions Vol1 Further Mathematics examination.

Gce Model Questions Vol1 2024 Further Mathematics Objective / Multiple Choice Hard Difficulty
Question 42 GCE_MODEL_QUESTIONS_VOL1 • 2024 • FURTHER_MATHEMATICS • objective

A uniform rod AB of length \(4\text{ m}\) and weight \(120\text{ N}\) is hinged at A to a vertical wall. The rod is held in equilibrium making an angle of \(30^{\circ}\) above the horizontal. A cable attached to B makes an angle \(\theta\) with the horizontal and is in tension of \(200\text{ N}\). (i) Find \(\theta\) (to the nearest tenth of a degree). (ii) Determine the magnitude and direction of the reaction force at the hinge A.

Answer Options

A. θ ≈ 60.2°; reaction ≈ 130 N acting 5.0° above the horizontal away from the wall (components Rx ≈ 129 N, Ry ≈ 11 N).
B. θ ≈ 45.1°; reaction ≈ 200 N acting 15.0° below the horizontal towards the wall (components Rx ≈ -193 N, Ry ≈ -52 N).
C. θ ≈ 30.0°; reaction ≈ 180 N acting 12.5° below the horizontal towards the wall (components Rx ≈ -175 N, Ry ≈ -39 N).
Correct Answer D. θ ≈ 45.1°; reaction ≈ 143 N acting 8.8° below the horizontal towards the wall (components Rx ≈ -141.3 N, Ry ≈ -21.8 N).
Correct Answer
D
Correct Option:
θ ≈ 45.1°; reaction ≈ 143 N acting 8.8° below the horizontal towards the wall (components Rx ≈ -141.3 N, Ry ≈ -21.8 N).

About This Question

This is Gce Model Questions Vol1 2024 Further Mathematics Question 42. It is one of the objective questions from the 2024 Gce Model Questions Vol1 Further Mathematics examination.

Difficulty level: Hard .

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