4. Two light elastic strings, each of length \(l \mathrm {~m}\) and modulus of elasticity \(\lambda \mathrm { N }\),are attached to a particle \(P\) of mass \(m \mathrm {~kg}\). The other ends of the strings are attached to fixed points \(A\) and \(B\) on the same horizontal level,
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where \(A B = 2 l \mathrm {~m} . P\) is held vertically below the mid-point of \(A B\), with each string taut and inclined at \(30 ^ { \circ }\) to the horizontal, and released from rest. Given that \(P\) comes to instantaneous rest when each string makes an angle of \(60 ^ { \circ }\) with the horizontal, show that \(\lambda = \frac { 3 m g } { 6 - 2 \sqrt { } 3 }\). \section*{MECHANICS 3 (A) TEST PAPER 8 Page 2}