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A rod AB of mass M and length 8l lies on...

A rod `AB` of mass `M` and length `8l` lies on a smooth horizontal surface. A particle, of `A` mass `m` and velocity `v_(0)` strike's the rod perpendicular to its length, as shown in Fig. As a result of the collision, the centre of mass of the rod attains a speed of `v_(0)//8` and the particle rebounds back with a (not to scale) speed of `v_(0)//4`. Find the following: a. The ratio `M//m`. b. The angular velocity of the rod about `O`. c. The coefficient of restitution `'e'` for the collision. d. The velocities of the ends `'A'` and `'B'` of the rod, namely, `v_(A)` and `v_(B)` respectively.

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