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There is a plank hinged about a point O. At the free end of the plank a small impulse is given. Will the plank perform pure rotation or both rotation and translation?

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how can it translate if it is hinged? Isn't the hinge fixed to a wall or something? Are you talking about the center of mass? How do you push it, sideways, at an angle? Is the hinge in a plane? This question is vague. Generally a free plank will both translate or rotate when pushed, but a hinged plack will only rotate around the hinge. Whether you consider that translation depends on whether you are considering the center of mass motion or the hinge point motion. –  Ron Maimon Aug 1 '12 at 8:42
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up vote 1 down vote accepted

Both Rotation and Translation. It will execute neither pure rotation nor pure translation

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While this is formally correct it comes without explanation of how it was arrived at at does not improve on Ron's comment. –  dmckee Aug 17 '12 at 14:07
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