24P3Q04

4a)

The centre of gravity of an object is the point at which the entire weight of the object appears to act.

4b)

Take moments about hinge:

Fig. 4.1: $\displaystyle W\times x=12\times 3.0\quad \cdots \cdots (1)$

Fig. 4.2: $\displaystyle W\times (3.0-x)=16\times 3.0\quad \cdots \cdots (2)$

(1)+(2): $\displaystyle \begin{aligned}W\times x=28\times 3.0 W&=28\text{ N}\end{aligned}$

Sub. Into (1): $\displaystyle \begin{aligned}28\times x&=12\times 3.0 x&=1.29\text{ m}\end{aligned}$

4c)

Same.

The perpendicular distances of W and F are now both shorter by the same factor of cos30°.

The ratio of the perpendicular distances is thus unchanged.

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