7 A bead, \(A\), of mass 0.1 kg is threaded on a long straight rigid wire which is inclined at \(\sin ^ { - 1 } \left( \frac { 7 } { 25 } \right)\) to the horizontal. \(A\) is released from rest and moves down the wire. The coefficient of friction between \(A\) and the wire is \(\mu\). When \(A\) has travelled 0.45 m down the wire, its speed is \(0.6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).

1. Show that \(\mu = 0.25\).
   Another bead, \(B\), of mass 0.5 kg is also threaded on the wire. At the point where \(A\) has travelled 0.45 m down the wire, it hits \(B\) which is instantaneously at rest on the wire. \(A\) is brought to instantaneous rest in the collision. The coefficient of friction between \(B\) and the wire is 0.275 .
2. Find the time from when the collision occurs until \(A\) collides with \(B\) again.
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