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A thin uniform rod AB of mass M and length L is hinged at one end A to the horizontal floor. Initially it stands vertically.It is allowed to fall freely in a vertical plane.If the linear speed of B when it hits the floor is  xgL,what is x?


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Solution

When the end B hits the floor,the vertical distance through which C( the mid point) falls is L/2.
From the law of conservation of energy, Loss of P.E=Loss of K.E.

MgL2 =12Iω2=12ML23ω2 3gL

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