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A uniform rod of m mass is hinged at and kept one end at initially vertical at rest. It is disturbed slightly. The hinge force when rod is about to hit ground.

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a

$\frac{\sqrt{41}}{4} m g$

b

$\frac{1}{4} m g$

c

$\frac{\sqrt{37}}{4} m g$

d

$\frac{3}{2} m g$

answer is C.

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Detailed Solution

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Final angular velocity (Mechanical energy is Conserved)
$\frac{1}{2} \cdot \frac{m l^{2}}{3} ω^{2} = M g \frac{l}{2}$
$\Rightarrow ω^{2} \frac{l}{2} = \frac{3 g}{2}$
Angular acceleration
$M g \frac{l}{2} = \frac{m l^{2}}{3} α \Rightarrow α \frac{l}{2} = \frac{3 g}{4}$
$H_{x} = \frac{3 m g}{2}, H_{y} = \frac{m g}{4} \Rightarrow H = \frac{\sqrt{37}}{4} m g$

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