Question:
A thin uniform rod of length $l$ and mass $m$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega$. Its centre of mass rises to a maximum height of
A thin uniform rod of length $l$ and mass $m$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega$. Its centre of mass rises to a maximum height of
Updated On: Jul 27, 2022
- $\frac{1}{3} \frac{\ell^{2}\omega^{2}}{g} $
- $\frac{1}{6} \frac{\ell\omega}{g} $
- $\frac{1}{2} \frac{\ell^{2}\omega^{2}}{g} $
- $\frac{1}{6} \frac{\ell^{2}\omega^{2}}{g} $
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The Correct Option is D
Solution and Explanation
$T.E_{i}=T.E_{f}$
$\frac{1}{2}I\omega^{2}=mgh$
$\frac{1}{2}\times\frac{1}{3}m\ell^{2}\omega^{2}=mgh \Rightarrow h=\frac{1}{6} \frac{\ell^{2}\omega^{2}}{g}$
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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.
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