Question:
A slender uniform rod of mass $M$ and length $l$ is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle $\theta$ with the vertical is :
A slender uniform rod of mass $M$ and length $l$ is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle $\theta$ with the vertical is :
Updated On: Sep 27, 2024
- $\frac{3g}{2 l} \sin \, \theta$
- $\frac{2g}{3l} \sin \, \theta$
- $\frac{3g}{2l} \cos\, \theta$
- $\frac{2g}{2l} \sin\, \theta$
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The Correct Option is A
Solution and Explanation
Torque at angle $\theta$
$\tau = Mg \, \sin \, \theta .$
$\tau = Mg \, \sin \, \theta .$
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Concepts Used:
System of Particles and Rotational Motion
- The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
- The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.