A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity \(\omega\). The force exerted by the liquid at the other end is :
- \(\frac{(ML\omega^2)}{(2)}\)
- \(\frac{(ML^2\omega)}{(2)}\)
- 2ML\(\omega\)2
- \(\frac{(ML^2\omega^2)}{(2)}\)
The Correct Option is A
Solution and Explanation
The centripetal force resulting from rotation is the force generated by the liquid at the other end.
The situation can be thought of as the liquid's centre of mass rotating at a distance of\(\frac{L}{2}\) from the axis of rotation.
As a result, the liquid exerts force at the end.
=\(M\omega^2\big(\frac{L}{2}\big)\) = \(\frac{(ML\omega^2)}{(2)}\)
Therefore, the correct option is (A): \(\frac{(ML\omega^2)}{(2)}\)
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Concepts Used:
Laws of Motion
The laws of motion, which are the keystone of classical mechanics, are three statements that defined the relationships between the forces acting on a body and its motion. They were first disclosed by English physicist and mathematician Isaac Newton.
Newton’s First Law of Motion
Newton’s 1st law states that a body at rest or uniform motion will continue to be at rest or uniform motion until and unless a net external force acts on it.
Newton’s Second Law of Motion
Newton's 2nd law of motion deals with the relation between force and acceleration. According to the second law of motion, the acceleration of an object as built by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
Newton’s Third Law of Motion
Newton's 3rd law of motion states when a body applies a force on another body that there is an equal and opposite reaction for every action.