3 A circular disc is rotating in a horizontal plane with angular speed \(16 \mathrm { rad } \mathrm { s } ^ { - 1 }\) about a fixed vertical axis passing through its centre \(O\). The moment of inertia of the disc about the axis is \(0.9 \mathrm {~kg} \mathrm {~m} ^ { 2 }\). A particle, initially at rest just above the surface of the disc, drops onto the disc and sticks to it at a point 0.4 m from \(O\). Afterwards, the angular speed of the disc with the particle attached is \(15 \mathrm { rad } \mathrm { s } ^ { - 1 }\).
- Find the mass of the particle.
- Find the loss of kinetic energy.