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# A thin uniform rod of mass m and length l is rotate about its upper end. When it is at rest, it receives an impulse J at its lowest point normal to its length. Immediately after impact, 1) the angular mometum of the rod is $JL$ 2) the angular velocity of the rod is $\large\frac{3J}{ml}$ 3) the kinetic energy of the rod is $\large\frac{3J^2}{2m}$ 4) the linear velocity of the midpoint of the rod is $\large\frac{3J}{3m}$ Which of the following is correct?

a) 1,2 and 3

b) 2,3 and 4

c) 1,3 and 4

d) all the above

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