WAEC 2019 · Paper 2 · Q6

(a)
A uniform beam $WX$ , of length $90\text{ cm}$ and weight $50\text{ N}$ , is suspended on a pivot $35\text{ cm}$ from $W$ . It is kept in equilibrium by means of forces $T$ and $20\text{ N}$ applied at $Y$ and $Z$ respectively. $|WY| = 10\text{ cm}$ and $|XZ| = 10\text{ cm}$ . Find the value of $T$ .

Worked solution (try it first)

From the pivot (35 cm from $W$ ): $T$ at $Y$ is $25$ cm on the $W$ side.
The weight, at the middle (45 cm from $W$ ), is $10$ cm on the $X$ side.
The 20 N at $Z$ (80 cm from $W$ ) is $45$ cm on the $X$ side.
Moments about the pivot: $25T = 50 \times 10 + 20 \times 45 = 1400$ , so $T = 56\text{ N}$ .