Mathematics 9709 · AS & A Level · Representation of data

Representation of data — practice question

A uniform lamina $ABCDE$ is made up of a rectangle $BCDE$ together with an isosceles triangle $ABE$, the two sharing the side $BE$. For the triangle, $AB = AE$, $BE = a\,\text{m}$ and the perpendicular height is $h\,\text{m}$. For the rectangle, $BC = DE = 0.5\,\text{m}$ and $CD = BE = a\,\text{m}$ (see diagram).
(i)[4]

Show that the centre of mass of the lamina is $\frac{3 - 4h^2}{12 + 12h}$ metres from $BE$ towards $CD$.

(ii)[2]

The lamina is suspended freely at $E$ and settles in equilibrium. If $DE$ is horizontal, find $h$.

(iii)[3]

If instead $h = 0.5$ and $AE$ is horizontal, determine $a$.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Apply the table of moments method

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