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  4. A uniform rod hinged at its one end is allowed to rotate in vertical plane. Rod is given an angular velocity ω in its vertical position as shown in figure. The value of w for which the force exerted by the hinge on rod is zero in this position is: <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/physics/a5637b80dd189c30600db3cb5ed12532-.png />

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Q. A uniform rod hinged at its one end is allowed to rotate in vertical plane. Rod is given an angular velocity $\omega$ in its vertical position as shown in figure. The value of $w$ for which the force exerted by the hinge on rod is zero in this position is:
image

System of Particles and Rotational Motion

Solution:

For the circular motion of com :
image
$mg = m \left(\frac{L}{2}\right) \omega^{2}$
$\Rightarrow \omega=\sqrt{\frac{2g}{L}}$