A tube of length 50 cm is filled completely with an incompressible… | JEE Main 2022 (29 Jul, Shift 2)

Q22JEE Main 2022 · 29 JUL · SHIFT 2Difficult

Bernoulli's Equation

A tube of length $50\text{ cm}$ is filled completely with an incompressible liquid of mass $250\text{ g}$ and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity $x\sqrt{F}\text{ rad s}^{-1}$ . If $F$ be the force exerted by the liquid at the other end then the value of $x$ will be __________.

Numerical answer type. Work it out, then open the answer.

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Answer: 4

The liquid moves in a circle; the end wall supplies the total centripetal force, acting on the centre of mass at $\frac{L}{2}$ .
$F = m\omega^2\frac{L}{2} = (0.25)\omega^2(0.25) = \frac{\omega^2}{16}$
$\omega = 4\sqrt{F}\text{ rad/s}$
So $x = 4$ .

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