A tube of length 50 cm is filled completely with an incompressible liquid of mass 250 g and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity x√F rad s−1. If F be the force exerted by the liquid at the other end then the value of x will be______.
Correct Answer: 4
Solution and Explanation
\(Fc=\frac{mω^2l}{2}\)
\(\frac{mω^2l}{2}=F\)
\(ω=\sqrt{\frac{2F}{\frac{1}{2}×\frac{1}{4}}}\)
ω=√16F
ω=4√F
Given that uniform angular velocity x√F rad s−1.
On comparing, x = 4
So, the answer is 4.
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Concepts Used:
Center of Mass
The center of mass of a body or system of a particle is defined as a point where the whole of the mass of the body or all the masses of a set of particles appeared to be concentrated.
The formula for the Centre of Mass:
Center of Gravity
The imaginary point through which on an object or a system, the force of Gravity is acted upon is known as the Centre of Gravity of that system. Usually, it is assumed while doing mechanical problems that the gravitational field is uniform which means that the Centre of Gravity and the Centre of Mass is at the same position.