Gce Model Questions Vol1 2025 Further Mathematics Question 44

Practice objective / multiple choice question 44 from the 2025 Gce Model Questions Vol1 Further Mathematics examination.

Gce Model Questions Vol1 2025 Further Mathematics Objective / Multiple Choice Hard Difficulty
Question 44 GCE_MODEL_QUESTIONS_VOL1 • 2025 • FURTHER_MATHEMATICS • objective

A uniform beam AB of length 6 m and weight 120 N is hinged at A to a vertical wall. The beam is held horizontal by a cable attached at B and anchored to a point C on the wall directly above A, the cable making an angle of \(30^{\circ}\) with the beam. A horizontal force of 80 N is applied at a point D located 2 m from A towards B. Determine (i) the tension in the cable, (ii) the horizontal reaction at the hinge, and (iii) the minimum coefficient of static friction \(\mu\) at the hinge required to prevent slipping, assuming the hinge can supply a frictional force up to \(\mu\) times the horizontal reaction.

Answer Options

A. T = 120 N; horizontal reaction = 80 + 50\sqrt3 N; \(\mu_{\min}=\dfrac{50}{80+50\sqrt3}\approx0.30\)
B. T = 120 N; horizontal reaction = 80 + 60\sqrt3 N; \(\mu_{\min}=\dfrac{60}{80+60\sqrt3}\approx0.25\)
Correct Answer C. T = 120 N; horizontal reaction = 80 + 60√3 N; \(\mu_{\min}=\dfrac{60}{80+60\sqrt3}\approx0.33\)
D. T = 100 N; horizontal reaction = 80 + 60\sqrt3 N; \(\mu_{\min}=\dfrac{60}{80+60\sqrt3}\approx0.33\)
Correct Answer
C
Correct Option:
T = 120 N; horizontal reaction = 80 + 60√3 N; \(\mu_{\min}=\dfrac{60}{80+60\sqrt3}\approx0.33\)

About This Question

This is Gce Model Questions Vol1 2025 Further Mathematics Question 44. It is one of the objective questions from the 2025 Gce Model Questions Vol1 Further Mathematics examination.

Difficulty level: Hard .

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