Question:
A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is $5\, cm$ and its rotational speed is $2$ rotations per second, then the difference in the heights between the centre and the sides, in $cm$, will be
A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is $5\, cm$ and its rotational speed is $2$ rotations per second, then the difference in the heights between the centre and the sides, in $cm$, will be
Updated On: Sep 27, 2024
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The Correct Option is C
Solution and Explanation
$y \, = \, \frac{\omega^2 \, x^2}{2g} \, = \, \frac{(2 \times 2\pi)^2 \times(0.05)^2}{20}] \, \, \simeq \, 2 \, cm $
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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.