5
\includegraphics[max width=\textwidth, alt={}, center]{dd23f4a8-f7e7-4f80-bad6-7e9ec21565fc-3_729_739_868_703} A particle \(P\) of mass 0.2 kg is attached to one end of each of two light inextensible strings, one of length 0.4 m and one of length 0.3 m . The other end of the longer string is attached to a fixed point \(A\), and the other end of the shorter string is attached to a fixed point \(B\), which is vertically below \(A\). The particle moves in a horizontal circle of radius 0.24 m at a constant angular speed of \(8 \mathrm { rad } \mathrm { s } ^ { - 1 }\) (see diagram). Both strings are taut, the tension in \(A P\) is \(S \mathrm {~N}\) and the tension in \(B P\) is \(T \mathrm {~N}\).

1. By resolving vertically, show that \(4 S = 3 T + 9.8\).
2. Find another equation connecting \(S\) and \(T\) and hence calculate the tensions, correct to 1 decimal place. \section*{[Questions 6 and 7 are printed overleaf.]}