A uniform rod of length $ L $ is fixed at one end. It is initially held vertically upward, then released. Find the vertical reaction at hinge when it becomes horizontal.

Question

A uniform rod of length $ L $ is fixed at one end. It is initially held vertically upward, then released. Find the vertical reaction at hinge when it becomes horizontal., $ \frac{m g}{2} $, $ \frac{m g}{3} $, $ \frac{3 m g}{2} $, $ \frac{m g}{4} $

MARKS App · Accepted Answer

m g - N y = m a y a y = Acceleration of the center of mass in y -direction. = L 2 × α (Since it is tangential acceleration) Now, N y = m g - m L α 2 But, α = τ A I A = m g L 2 m L 2 3 = 3 g 2 L So, N y = m g - m L 2 × 3 g 2 L = m g 4

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