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:

Question

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" /> (A) √(g/L) (B) √(2 g/L) (C) √(g/2 L) (D) √(3 g/L)

Tardigrade Admin · Accepted Answer

For the circular motion of com: <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/c0fbf46be84ec0baa306346445ad338f-.png" /> mg = m ((L/2)) ω2 ⇒ ω=√(2g/L)

Q. 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:

$\frac{g}{L}$

$\frac{2 g}{L}$

$\frac{g}{2 L}$

$\frac{3 g}{L}$

For the circular motion of com :

$m g = m (\frac{L}{2}) ω^{2}$
$\Rightarrow ω = \frac{2 g}{L}$

Q. 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:

Lg​​

L2g​​

2Lg​​

L3g​​