WAEC 2022 · Paper 2 · Q7

(a)
A body of mass $1.5\text{ kg}$ is suspended by two light inextensible ropes inclined at $30^\circ$ and $60^\circ$ to the horizontal. Calculate the tensions in the ropes. $[\text{Take } g = 10\text{ m s}^{-2}]$
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

The weight is $1.5 \times 10 = 15\text{ N}$ .
The ropes meet at $180^\circ - 30^\circ - 60^\circ = 90^\circ$ .
The rope at $30^\circ$ makes $120^\circ$ with the weight.
The rope at $60^\circ$ makes $150^\circ$ .
Lami: $\dfrac{T_1}{\sin150^\circ} = \dfrac{T_2}{\sin120^\circ}$
$= \dfrac{15}{\sin90^\circ}$ .
$T_1 = 15\sin150^\circ = 7.5\text{ N}$ (the rope at $30^\circ$ ).
$T_2 = 15\sin120^\circ$
$\approx 12.99\text{ N}$ (the rope at $60^\circ$ ).