A disc of mass 1 kg and radius… - JEE Main 2022 Physics PYQ

JEE Main 2022 — Physics Mechanics

2022integerhard

A disc of mass $1\mathrm{kg}$ and radius $R$ is free of rotate about a horizontal axis passing through its centre and perpendicular to the plane of disc. A body of same mass as that of disc is fixed at the highest point of the disc. Now the system is released, when the body comes to the lowest position, its angular speed will be $4\sqrt{\frac{x}{3R}}\mathrm{rad}{s}^{-1}$ where $x=$ _____ .

Official previous-year question

Held on 26 Jul 2022 · Verified 6 Jul 2026.

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Solution

Let the angular speed of disc be $\omega$ .

JEE Main 2022 Physics, Rotational Motion — solution figure

Using conservation of mechanical energy

$mg2R=\frac{1}{2}{I}_{\mathrm{disc}}{\omega }^{2}+\frac{1}{2}{I}_{\mathrm{particle}}{\omega }^{2}$

Where, $I$ is moment of inertia.

$\Rightarrow mg2R=\frac{{\omega }^{2}}{2}[\frac{{m}^{2}}{2}+m{R}^{2}]$

$\Rightarrow mg2R=\frac{{\omega }^{2}}{2}(\frac{3}{2}m{R}^{2})$

$\Rightarrow \frac{3}{4}{\omega }^{2}=\frac{2g}{R}$

$\Rightarrow {\omega }^{2}=\frac{8g}{3R}$

Thus, angular speed is $\omega =\sqrt{\frac{80}{3R}}\mathrm{rad}{s}^{-1}$

Given $\omega =4\sqrt{\frac{x}{3R}}$

Comparing both, $16\frac{x}{3R}=\frac{80}{3R}$

Therefore, the value of $x=5$ .

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Solution

Let the angular speed of disc be $\omega$ .

JEE Main 2022 Physics, Rotational Motion — solution figure

Using conservation of mechanical energy

$mg2R=\frac{1}{2}{I}_{\mathrm{disc}}{\omega }^{2}+\frac{1}{2}{I}_{\mathrm{particle}}{\omega }^{2}$

Where, $I$ is moment of inertia.

$\Rightarrow mg2R=\frac{{\omega }^{2}}{2}[\frac{{m}^{2}}{2}+m{R}^{2}]$

$\Rightarrow mg2R=\frac{{\omega }^{2}}{2}(\frac{3}{2}m{R}^{2})$

$\Rightarrow \frac{3}{4}{\omega }^{2}=\frac{2g}{R}$

$\Rightarrow {\omega }^{2}=\frac{8g}{3R}$

Thus, angular speed is $\omega =\sqrt{\frac{80}{3R}}\mathrm{rad}{s}^{-1}$

Given $\omega =4\sqrt{\frac{x}{3R}}$

Comparing both, $16\frac{x}{3R}=\frac{80}{3R}$

Therefore, the value of $x=5$ .

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Solution

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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