First slide

Kinematics of rotational motion about fixed axis

Question

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

Moderate

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

Solution

Just after the string is burnt, weight mg produces a moment about the hinge and clockwise angular acceleration $α = \frac{m g \frac{l}{2}}{\frac{1}{3} m l^{2}} = \frac{3 g}{l}$
So a vertically upward pseudo force $m . (α \frac{l}{2})$ 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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