7 A particle \(P\) is attached to one end of a light elastic string of natural length 1.2 m and modulus of elasticity 12 N . The other end of the string is attached to a fixed point \(O\) on a smooth plane inclined at an angle of \(30 ^ { \circ }\) to the horizontal. \(P\) rests in equilibrium on the plane, 1.6 m from \(O\).

1. Calculate the mass of \(P\). A particle \(Q\), with mass equal to the mass of \(P\), is projected up the plane along a line of greatest slope. When \(Q\) strikes \(P\) the two particles coalesce. The combined particle remains attached to the string and moves up the plane, coming to instantaneous rest after moving 0.2 m .
2. Show that the initial kinetic energy of the combined particle is 1 J . The combined particle subsequently moves down the plane.
3. Calculate the greatest speed of the combined particle in the subsequent motion. \footnotetext{Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. To avoid the issue of disclosure of answer-related information to candidates, all copyright acknowledgements are reproduced online in the Cambridge International Examinations Copyright Acknowledgements Booklet. This is produced for each series of examinations and is freely available to download at \href{http://www.cie.org.uk}{www.cie.org.uk} after the live examination series. Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. }