Question

Rod is hanging vertically in state of rest. Hinge
reaction on the rod is
Hinged​

Answer 1

Thus the angular velocity of the rod is w = √24g / 7 L

Explanation:

Correct statement:

A uniform rod is hinged as shown in the figure and is released from a horizontal position. The angular velocity of the rod as it passes the vertical position is:

Solution:

• MOL of the rod about the hinge point is  
• Io = ML^2 / 12  + M (L / 4)^2
• Io = 7 ML^2 / 48
• Now when the rod is in vertical position the hinge would be in the vertical position.
• The center of mass = L / 4
• Now by the law of conservation of energy.
• mg (L/4)  = 1 / 2  Iow^2
• mgL/4 =  1 / 2 x 7 ML^2 / 48 w^2
• w = √24g / 7 L