A uniform rectangular lamina ABCD has $AD = BC = 2a$ and $AB = DC = a$ . Vertex A rests on a horizontal table and a force $P$ acts along the side DC. When moments are taken about A, what is the perpendicular distance from A to the line of action of $P$ ?

\dfrac{a}{2}

, because the force acts through the centre of the lamina rather than along an edge.

2a

, because DC is the side parallel to AB and the sides AB and DC are

AD = 2a

apart.

a

, because

a

is the length of the side DC along which the force is acting.

a\sqrt{5}

, because that is the length of the diagonal AC of the rectangle.

Explanation

In rectangle ABCD the sides AB and DC are opposite each other and are separated by the length of AD, which is

2a

. A is a point on AB, so the perpendicular distance from A to the whole line DC is

2a

, whatever the angle at which the lamina is tilted. The length of DC itself is irrelevant to a moment about A.

Derived from ZIMSEC Additional Mathematics Paper 2, Specimen Paper, Q2

More questions from this paper