A tube of length 50 cm is… - JEE Main 2022 Physics PYQ

JEE Main 2022 — Physics Mechanics

2022integerhard

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

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Held on 29 Jul 2022 · Verified 6 Jul 2026.

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Solution

Considering an element of tube of length $dx$ having mass $dm$ at a distance of $x$ from right end as shown in figure below.

JEE Main 2022 Physics, Laws of Motion — solution figure

Now, force acting of that element is $\displaystyle F=\int (dm){\omega }^{2}x$

Integrating the above relation for whole length of tube, we have

$F={\int }_{0}^{L}(\frac{m}{L}dx){\omega }^{2}x$

$=\frac{m}{L}{\omega }^{2}\frac{{L}^{2}}{2}$ $=\frac{m{\omega }^{2}L}{2}$

$\Rightarrow \omega =\sqrt{\frac{2}{mL}}\sqrt{F}$ $=\sqrt{\frac{2}{0.25\times 0.5}}\sqrt{F}$

$=\sqrt{16}\sqrt{F}$ $=4\sqrt{F}\mathrm{rad}{s}^{-1}$

Hence, the value of $x=4$ .

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Solution

Considering an element of tube of length $dx$ having mass $dm$ at a distance of $x$ from right end as shown in figure below.

JEE Main 2022 Physics, Laws of Motion — solution figure

Now, force acting of that element is $\displaystyle F=\int (dm){\omega }^{2}x$

Integrating the above relation for whole length of tube, we have

$F={\int }_{0}^{L}(\frac{m}{L}dx){\omega }^{2}x$

$=\frac{m}{L}{\omega }^{2}\frac{{L}^{2}}{2}$ $=\frac{m{\omega }^{2}L}{2}$

$\Rightarrow \omega =\sqrt{\frac{2}{mL}}\sqrt{F}$ $=\sqrt{\frac{2}{0.25\times 0.5}}\sqrt{F}$

$=\sqrt{16}\sqrt{F}$ $=4\sqrt{F}\mathrm{rad}{s}^{-1}$

Hence, the value of $x=4$ .

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Solution

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JEE Main Mechanics in other years

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Did you get this right?

Solution

Your note

JEE Main Mechanics in other years

More JEE Main Mechanics questions

Other Physics topics for JEE Main

Electromagnetism

Modern Physics

Optics

Thermodynamics

Waves & Oscillations

Keep practicing Mechanics