Question

The horizontal beam in figure weights $150N$, and its centre of gravity is at its centre. Find the horizontal and vertical component of the forces exerted on the beam at the wall.

• A. Horizontal component is $500N$ towards left and vertical component $75N$ downwards
• B. Horizontal component is $500N$ towards right and vertical component $75N$
• C. Horizontal component is $625N$ towards left and vertical component $150N$
• D. Horizontal component is $625N$ towards right and vertical component $150N$ downwards

Answer 1

Answer: (B)

Horizontal component is $500N$ towards right and vertical component $75N$

Net torque on the beam about hinge is zero.

Let the horizontal component & vertical component of tension be $T_H,T_V$ respectively. & the horizontal component & vertical component of forces exerted on the beam at the wall be $F_H,F_V$ respectively

$\therefore T_V\times 4-300\times 4-150\times 2=0T_V=375N$ (upwards)

By geometry relation between $T_H,T_V$

$\frac{T_V}{T_H}=\frac{3}{4}\therefore T_H=400N$ (left)

Force Balance equations:

$F_H{+T}_H=0F_H=500N\left(right\right)$

$F_V{+T}_V-300-150=0F_V=450-375=75N\left(upwards\right)$