A rod of length L is hinged from one end. It is brought to a horizontal position and released. The angular velocity of the rod, when it is in vertical position is

Question

A rod of length L is hinged from one end. It is brought to a horizontal position and released. The angular velocity of the rod, when it is in vertical position is (A) √(2 g/L) (B) √(3 g/L) (C) √(g/2 L) (D) √(g/L)

Tardigrade Admin · Accepted Answer

The rod in potential energy = gain in kinetic energy <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/9111d5b293ec563c05cab751bdb98acb-.png" /> ⇒ m g (L/2)=(1/2)((m L2/3)) ω2 ⇒ ω=√(3 g/L)

Q. A rod of length $L$ is hinged from one end. It is brought to a horizontal position and released. The angular velocity of the rod, when it is in vertical position is

$\frac{2 g}{L}$

$\frac{3 g}{L}$

$\frac{g}{2 L}$

$\frac{g}{L}$

The rod in potential energy $=$ gain in kinetic energy

$\Rightarrow m g \frac{L}{2} = \frac{1}{2} (\frac{m L ^{2}}{3}) ω^{2}$
$\Rightarrow ω = \frac{3 g}{L}$

Q. A rod of length L is hinged from one end. It is brought to a horizontal position and released. The angular velocity of the rod, when it is in vertical position is

L2g​​

L3g​​

2Lg​​

Lg​​