A ring of mass 4kg is threaded on a smooth circular rigid wire with centre C. The wire is fixed in a vertical plane and the ring is kept at rest by a light string connected to A, the highest point of the circle. The string makes an angle of 25° to the vertical (see diagram). Find the tension in the string and the magnitude of the normal reaction of the wire on the ring. [Figure X.X]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

1. [M1] T cos 25 = 40 + R cos 50 Resolving in any direction e.g. horizontal, vertical, along radius or tangent.
2. [M1] R sin 50 = T sin 25 Resolving in a second direction.
3. [A1] Radially: T cos 25 = R + 40 cos 50 Tangentially: T sin 25 = 40 sin 50 Parallel to T: T = R cos 25 + 40 cos 25 Perpendicular to T: R sin 25 = 40 sin 25 Vertically: T cos 25 = 40 + R cos 50 Horizontally: R sin 50 = T sin 25 Two correct equations.
4. [M1] Solving equation(s) to find either Tor R
5. [A1] T = 72.5 N From 72.504....
6. [A1] R = 40 N