JEE Main 2020 Physics, Rotational Motion — question figure A… - JEE Main 2020 Physics PYQ

JEE Main 2020 — Physics Mechanics

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JEE Main 2020 Physics, Rotational Motion — question figure

A uniform rod of length ' ${\ell }^{'}$ is pivoted at one of its ends on a vertical shaft of negligible radius. When the shaft rotates at angular speed $\omega$ the rod makes an angle $\theta$ with it (see figure). To find $\theta$ equate the rate of change of angular momentum (direction going into the paper) $\frac{m{\ell }^{2}}{12}{\omega }^{2}\mathrm{sin}\theta$ about the centre of mass (CM) to the torque provided by the horizontal and vertical forces ${F}_{H}$ and ${F}_{v}$ about the CM. The value of $\theta$ is then such that:

Official previous-year question

Held on 3 Sept 2020 · Verified 6 Jul 2026.

Options

A
$\mathrm{cos}\theta =\frac{2g}{3l{\omega }^{2}}$
B
$\mathrm{cos}\theta =\frac{g}{2\ell {\omega }^{2}}$
C
$cos\theta =\frac{g}{\ell {\omega }^{2}}$
D
$\mathrm{cos}\theta =\frac{3g}{2\ell {\omega }^{2}}$

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Solution

Torque of centrifugal force $\displaystyle {\tau }_{\mathrm{cf}}=\mathrm{dm}.x\mathrm{sin}{\text{θω}}^{2}\mathrm{xcos}\vartheta =\frac{m}{l}{\omega }^{2}\mathrm{sin}\theta cos\theta {\int }_{0}^{l}{x}^{2}\mathrm{dx}$

${\tau }_{\mathrm{ef}}=\frac{m{l}^{2}{\omega }^{2}sin\theta cos\theta }{3}$

${\tau }_{\mathrm{mg}}={\tau }_{\mathrm{cf}}$

$\mathrm{mg}.\frac{l}{2}\mathrm{sin}\theta =\frac{m{l}^{2}{\omega }^{2}sin\theta \mathrm{cos}\theta }{3}$

$\mathrm{cos}\theta =\frac{3g}{2l{\omega }^{2}}$

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Options

$\mathrm{cos}\theta =\frac{2g}{3l{\omega }^{2}}$

$\mathrm{cos}\theta =\frac{g}{2\ell {\omega }^{2}}$

$cos\theta =\frac{g}{\ell {\omega }^{2}}$

$\mathrm{cos}\theta =\frac{3g}{2\ell {\omega }^{2}}$

Solution

${\tau }_{\mathrm{ef}}=\frac{m{l}^{2}{\omega }^{2}sin\theta cos\theta }{3}$

${\tau }_{\mathrm{mg}}={\tau }_{\mathrm{cf}}$

$\mathrm{mg}.\frac{l}{2}\mathrm{sin}\theta =\frac{m{l}^{2}{\omega }^{2}sin\theta \mathrm{cos}\theta }{3}$

$\mathrm{cos}\theta =\frac{3g}{2l{\omega }^{2}}$

Options

Did you get this right?

Solution

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JEE Main Mechanics in other years

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Options

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