Mathematics 9709 · AS & A Level · Representation of data

Representation of data — practice question

A uniform lamina is formed by combining rectangle $ABCD$, where $AB = CD = 0.56\text{ m}$ and $BC = AD = 2\text{ m}$, with square $EFGA$ of side $1.2\text{ m}$. The square’s vertex $E$ lies on the side $AD$ of the rectangle (see diagram). The lamina’s centre of mass is $h\text{ m}$ from $BC$ and $v\text{ m}$ from $BAG$.
(i)[4]

Find the value of $h$, then show that $v = h$.

(ii)[1]

The lamina is freely suspended from point $B$ and comes to rest in equilibrium. State the angle made by edge $BC$ with the horizontal.

(iii)[2]

Now the lamina is freely suspended from point $F$ and is in equilibrium. Calculate the angle between $FG$ and the vertical.

Worked solution & mark scheme

This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: Taking moments about $BC$ gives $2\times0.56\times0.28 + 1.2^2(0.56+1.2/2)=h(2\times0.56+1.2^2)$

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