ABCD is a uniform square lamina with sides of length 0.6 m. A circular hole of radius r m is made in the lamina. The centre of the hole is 0.3 m from AB and 0.25 m from AD. The lamina is freely suspended at A and hangs with the axis of symmetry making an angle of 48° with the horizontal [Figure 7.1].

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2018). The mark or mark type is shown in brackets.

1. [M1] tan48 = x/0.3 x is the distance of the centre of mass from AD
2. [A1] x = 0.3332
3. [M1] 0.6² × 0.3 = πr² × 0.25 + (0.6² – πr²)x OR 0.6² × 0.3 = πr² × 0.35 + (0.6² – πr²) × (0.6−x) Take moments about AD Take moments about BC
4. [A1] πr² × (0.3332 – 0.25) = 0.6² × (0.3332 – 0.3) OR πr²(0.6 – 0.3332 – 0.35) = 0.6² (0.6 – 0.3332 – 0.3)
5. [AG] r = 0.214 A1
6. [M1] 0.3W=0.6 × 15cos60 Take moments about C.(W = weight of the lamina)
7. [A1] W = 15
8. [M1] Square = 15 × 0.6² / (0.6² – π × 0.214²) Recognise that the ratio of weights = ratio of areas
9. [A1] Square = 25(.0) N