M4 June 2013 (R) Q3

3. A smooth uniform sphere \(A\), of mass \(5m\) and radius \(r\), is at rest on a smooth horizontal plane. A second smooth uniform sphere \(B\), of mass \(3m\) and radius \(r\), is moving in a straight line on the plane with speed \(u\) m s\(^{-1}\) and strikes \(A\). Immediately before the impact the direction of motion of \(B\) makes an angle of 60\(^\circ\) with the line of centres of the spheres. The direction of motion of \(B\) is turned through an angle of 30\(^\circ\) by the impact.

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