Question 44
NECO
•
2020
•
FURTHER_MATHEMATICS
•
objective
A uniform beam \( AB \) 6 m long is hinged at \( A \) to a vertical wall. The beam makes an angle of \(30^{\circ}\) with the horizontal. A weight of 800 N is attached at point \( C \) which is 2 m from \( A \) along the beam. The beam is supported by a cable attached at \( B \) and anchored to a point \( D \) on the wall directly above \( A \) such that the cable makes an angle of \(45^{\circ}\) with the beam. Determine (i) the tension in the cable, (ii) the horizontal and vertical components of the reaction at the hinge \( A \), and (iii) the magnitude and direction of the resultant reaction at \( A \).
Answer Options
A.
Tension \( T=\frac{400\sqrt6}{2}\) N \(\approx 490\) N; Horizontal reaction \( H=\frac{600+200\sqrt3}{2}\) N \(\approx 473\) N; Vertical reaction \( V=\frac{1800+200\sqrt3}{2}\) N \(\approx 1073\) N; Resultant \( R\approx 1100\) N acting at \( \approx 70^{\circ}\) above the horizontal.
B.
Tension \( T=\frac{400\sqrt6}{5}\) N \(\approx 196\) N; Horizontal reaction \( H=\frac{600+200\sqrt3}{5}\) N \(\approx 189\) N; Vertical reaction \( V=\frac{1800+200\sqrt3}{5}\) N \(\approx 429\) N; Resultant \( R\approx 460\) N acting at \( \approx 55^{\circ}\) above the horizontal.
C.
Tension \( T=\frac{400\sqrt6}{4}\) N \(\approx 245\) N; Horizontal reaction \( H=\frac{600+200\sqrt3}{4}\) N \(\approx 237\) N; Vertical reaction \( V=\frac{1800+200\sqrt3}{4}\) N \(\approx 537\) N; Resultant \( R\approx 600\) N acting at \( \approx 60^{\circ}\) above the horizontal.
Correct Answer
D.
Tension \( T=\frac{400\sqrt6}{3}\) N \(\approx 327\) N; Horizontal reaction \( H=\frac{600+200\sqrt3}{3}\) N \(\approx 315\) N; Vertical reaction \( V=\frac{1800+200\sqrt3}{3}\) N \(\approx 715\) N; Resultant \( R\approx 782\) N acting at \( \approx 66.5^{\circ}\) above the horizontal.
Correct Answer
D
Correct Option:
Tension \( T=\frac{400\sqrt6}{3}\) N \(\approx 327\) N; Horizontal reaction \( H=\frac{600+200\sqrt3}{3}\) N \(\approx 315\) N; Vertical reaction \( V=\frac{1800+200\sqrt3}{3}\) N \(\approx 715\) N; Resultant \( R\approx 782\) N acting at \( \approx 66.5^{\circ}\) above the horizontal.
About This Question
This is
Neco
2020
Further Mathematics
Question 44.
It is one of the
objective
questions from the
2020
Neco
Further Mathematics
examination.
Difficulty level:
Hard
.