4. A small stone \(P\) of mass \(m \mathrm {~kg}\) is attached to one end of a light elastic string of modulus 3 mg N and natural length \(2 l \mathrm {~m}\). The other end of the string is fixed to a point \(O\) at a height \(3 l \mathrm {~m}\) above a horizontal surface. \(P\) is released from rest at \(O\); it hits the surface and rebounds to a height of \(2 l \mathrm {~m}\). The coefficient of restitution between \(P\) and the surface is \(e\).
Calculate the value of \(e\). State one assumption (other than the string being light) that you have used in your solution.
(1 mark) \section*{MECHANICS 3 (A) TEST PAPER 6 Page 2}