A uniform rod of mass M and length L is pivoted at one end and hangs as

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A uniform rod of mass M and length L is pivoted at one end and hangs as in Figure so that it is free to rotate without friction about its pivot. It is struck by a horizontal force F0 for a short time Δt at a distance x below the pivot as shown. 

(a) Show that the speed of the center of mass of the rod just after being struck is given by v0 = 3F0xΔt/2ML. 

(b) Find the force delivered by the pivot, and show that this force is zero if x = 2L/3.

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