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Q.

The end A of a thin rod AB of mass m and length l is hinged and the end B is attached to X string BC hanging from a ceiling. Just after the string is burnt

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a

angular acceleration of the rod is zero

b

angular acceleration of the rod is g/l

c

angular velocity of the rod is g/l2

d

reaction at the hinge A is less than mg

answer is D.

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Detailed Solution

Just after the string is burnt, weight mg produces a moment about the hinge and clockwise angular acceleration α=mg l213ml2=3glSo a vertically upward pseudo force m.αl2 acts on the rod as shown in figure. Because of the action of this pseudo force, N becomes less than mg.
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