3
\includegraphics[max width=\textwidth, alt={}, center]{d3609757-50ae-4c68-8992-4304867a2d84-3_456_511_260_817} A particle of mass 0.24 kg is attached to one end of a light inextensible string of length 2 m . The other end of the string is attached to a fixed point. The particle moves with constant speed in a horizontal circle. The string makes an angle \(\theta\) with the vertical (see diagram), and the tension in the string is \(T \mathrm {~N}\). The acceleration of the particle has magnitude \(7.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).

1. Show that \(\tan \theta = 0.75\) and find the value of \(T\).
2. Find the speed of the particle.