4. \begin{figure}[h] \end{figure} Figure 2 shows a light elastic string, of modulus of elasticity \(\lambda\) newtons and natural length 0.6 m . One end of the string is attached to a fixed point \(A\) on a rough plane which is inclined at \(30 ^ { \circ }\) to the horizontal. The other end of the string is attached to a particle \(P\) of mass 0.5 kg . The string lies along a line of greatest slope of the plane. The particle is held at rest on the plane at the point \(B\), where \(B\) is lower than \(A\) and \(A B = 1.2 \mathrm {~m}\). The particle then receives an impulse of magnitude 1.5 N s in the direction parallel to the string, causing \(P\) to move up the plane towards \(A\). The coefficient of friction between \(P\) and the plane is 0.7 . Given that \(P\) comes to rest at the instant when the string becomes slack, find the value of \(\lambda\).