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

Updated On: Jul 31, 2023
  • $ \sqrt{\frac{2g}{L}} $
  • $ \sqrt{\frac{3g}{L}} $
  • $ \sqrt{\frac{g}{2L}} $
  • $ \sqrt{\frac{g}{L}} $
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The Correct Option is B

Solution and Explanation

The rod in potential energy = gain in kinetic energy
$m g \frac{L}{2}=\frac{1}{2}\left(\frac{m L^{2}}{3}\right) \omega^{2}$ $\omega=\sqrt{\frac{3 g}{L}}$

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Concepts Used:

Rotational Motion

Rotational motion can be defined as the motion of an object around a circular path, in a fixed orbit.

Rotational Motion Examples:

The wheel or rotor of a motor, which appears in rotation motion problems, is a common example of the rotational motion of a rigid body.

Other examples:

  • Moving by Bus
  • Sailing of Boat
  • Dog walking
  • A person shaking the plant.
  • A stone falls straight at the surface of the earth.
  • Movement of a coin over a carrom board 

Types of Motion involving Rotation:

  1. Rotation about a fixed axis (Pure rotation)
  2. Rotation about an axis of rotation (Combined translational and rotational motion)
  3. Rotation about an axis in the rotation (rotating axis)