The diagram shows two particles \(A\) and \(B\) of masses \(\quantity{0.2}{kg}\) and \(\quantity{0.4}{kg}\) respectively lying on a rough slope inclined at an angle \(\theta\) to the horizontal where \(\tan\theta=\frac{3}{4}\). The coefficient of friction between the particles and the slope is \(\frac{1}{4}\). A light inextensible string joins \(A\) to \(B\) and the system is just maintained in equilibrium, with both particles about to move up the slope, by a force on \(B\) of \(\quantity{P\,}{N}\), acting up the slope.

[Take \(g\) to be \(\quantity{10}{m\,s^{-2}}\).]

Calculate

the value of \(P\),

the tension in the string.