A rod of mass m and length L, pivoted at one of its ends, is hanging vertically. A bullet of the same mass moving at speed v strikes the rod horizontally at a distance x from its pivoted end and gets embedded in it. The combined system now rotates with angular speed $$\omega$$ about the pivot. The maximum angular speed $$\omega$$ M is achieved for x = x M . Then

$$\omega = {{3vx} \over {{L^2} + 3{x^2}}}$$

$${\omega _M} = \frac{v}{2L} \sqrt{3}$$

$$\omega = {{12vx} \over {{L^2} + 12{x^2}}}$$

A thin and uniform rod of mass M and length L is held vertical on a floor with large friction. The rod is released from rest so that it falls by rotating about its contact-point with the floor without slipping. Which of the following statement(s) is/are correct, when the rod makes an angle 60$$^\circ $$ with vertical? [g is the acceleration due to gravity]

The normal reaction force from the floor on the rod will be $${{Mg} \over 16}$$.

The radial acceleration of the rod's center of mass will be $${{3g} \over 4}$$.

The angular speed of the rod will be $$\sqrt {{{3g} \over {2L}}} $$.

The angular acceleration of the rod will be $${{2g} \over L}$$.

Consider a body of mass $$1.0$$ $$kg$$ at rest at the origin at time $$t=0.$$ A force $$\overrightarrow F = \left( {\alpha t \widehat i + \beta \widehat j} \right)$$ is applied on the body, where $$\alpha = 1.0N{s^{ - 1}}$$ and $$\beta = 1.0\,N.$$ The torque acting on the body about the origin at time $$t=1.0s$$ is $$\overrightarrow \tau .$$ Which of the following statements is (are) true?

$$\left| {\overrightarrow \tau } \right| = {1 \over 3}\,Nm$$

The velocity of the body at $$t = 1s$$ is $$\overrightarrow v = {1 \over 2}\left( {\widehat i + 2\widehat j} \right)m{s^{ - 1}}$$

The torque $$\overrightarrow \tau $$ is in the direction of the unit vector $$ + \,\widehat k$$

The magnitude of displacement of the body at $$t = 1s$$ is $${1 \over 6}m$$

The potential energy of a particle of mass $$m$$ at a distance $$r$$ from a fixed point $$O$$ is given by $$V\left( r \right) = k{r^2}/2,$$ where $$k$$ is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius $$R$$ about the point $$O$$. If $$v$$ is the speed of the particle and $$L$$ is the magnitude of its angular momentum about $$O,$$ which of the following statements is (are) true?

$$v = \sqrt {{k \over {2m}}} R$$

$$L = \sqrt {{{mk} \over 2}} {R^2}$$

The position vector $$\overrightarrow r $$ of a particle of mass m is given by the following equation $$$\overrightarrow r \left( t \right) = \alpha {t^3}\widehat i + \beta {t^2}\widehat j,$$$where $$\alpha = {{10} \over 3}m{s^{ - 3}}$$, $$\beta = 5\,m{s^{ - 2}}$$ and m = 0.1 kg. At t = 1 s, which of the following statement(s) is(are) true about the particle?

The velocity $$\overrightarrow v $$ is given by $$\overrightarrow v = \left( {10\widehat i + 10\widehat j} \right)$$ ms -1

The angular momentum $$\overrightarrow L $$ with respect to the origin is given by $$\overrightarrow L = - \left( {{5 \over 3}} \right)\widehat k\,N\,m\,s$$

The torque $$\overrightarrow \tau $$ with respect to the origin is given by $$\overrightarrow \tau = - \left( {{{20} \over 3}} \right)\widehat k\,N\,m$$

The force $$\overrightarrow F $$ is given by $$\overrightarrow F = \left( {\widehat i + 2\widehat j} \right)N$$

Rotational Motion — JEE Advanced Previous Year Questions

36 solved PYQs · 2016–2026 · Physics

Solved PYQs: 36
Years covered: 2016–2026
Avg / year: ~3
Subject: Physics

How many JEE Advanced questions come from Rotational Motion?

Rotational Motion has contributed 36 questions to Joint Entrance Examination (Advanced) papers between 2016 and 2026 — an average of about 3 questions a year. That count is measured from EByAi’s bank of 18,502 JEE Advanced questions, not estimated from a syllabus. Every one of the 36 questions carries a written, step-by-step solution, and each is tagged to Rotational Motion within Physics, so you can drill this chapter across every year at once instead of hunting through paper PDFs. Practising a chapter’s full PYQ history is the fastest way to learn the patterns examiners reuse.

Sample Rotational Motion questions from real JEE Advanced papers

These are 5 real questions from the bank — exactly as asked, with the answer one tap away. All 36 Rotational Motion questions (with full written solutions) are available in practice.

Question 1 · JEE Advanced 2020 · one or more correct
A rod of mass m and length L, pivoted at one of its ends, is hanging vertically. A bullet of the same mass moving at speed v strikes the rod horizontally at a distance x from its pivoted end and gets embedded in it. The combined system now rotates with angular speed $ω$ about the pivot. The maximum angular speed $ω$ M is achieved for x = x M . Then
1. (A) $ω = \frac{3 v x}{L ^{2} + 3 x ^{2}}$
2. (B) $ω = \frac{12 v x}{L ^{2} + 12 x ^{2}}$
3. (C) $x_{M} = \frac{L}{3}$
4. (D) $ω_{M} = \frac{v}{2 L} 3$
Show answerAnswer
$Answer: options A and C and D$
Question 2 · JEE Advanced 2019 · one or more correct
A thin and uniform rod of mass M and length L is held vertical on a floor with large friction. The rod is released from rest so that it falls by rotating about its contact-point with the floor without slipping. Which of the following statement(s) is/are correct, when the rod makes an angle 60 $^{\circ}$ with vertical? [g is the acceleration due to gravity]
1. (A) $The angular acceleration of the rod will be \frac{2 g}{L} .$
2. (B) $The normal reaction force from the floor on the rod will be \frac{M g}{16} .$
3. (C) $The radial acceleration of the rod's center of mass will be \frac{3 g}{4} .$
4. (D) $The angular speed of the rod will be \frac{3 g}{2 L} .$
Show answerAnswer
$Answer: options B and C and D$
Question 3 · JEE Advanced 2018 · one or more correct
Consider a body of mass $1.0$ $k g$ at rest at the origin at time $t = 0.$ A force $F = (α t i + β j)$ is applied on the body, where $α = 1.0 N s^{- 1}$ and $β = 1.0 N .$ The torque acting on the body about the origin at time $t = 1.0 s$ is $τ .$ Which of the following statements is (are) true?
1. (A) $τ = \frac{1}{3} N m$
2. (B) $The torque τ is in the direction of the unit vector + k$
3. (C) $The velocity of the body at t = 1 s is v = \frac{1}{2} (i + 2 j) m s^{- 1}$
4. (D) $The magnitude of displacement of the body at t = 1 s is \frac{1}{6} m$
Show answerAnswer
$Answer: options A and C$
Question 4 · JEE Advanced 2018 · one or more correct
The potential energy of a particle of mass $m$ at a distance $r$ from a fixed point $O$ is given by $V (r) = k r^{2} /2,$ where $k$ is a positive constant of appropriate dimensions. This particle is moving in a circular orbit of radius $R$ about the point $O$ . If $v$ is the speed of the particle and $L$ is the magnitude of its angular momentum about $O,$ which of the following statements is (are) true?
1. (A) $v = \frac{k}{2 m} R$
2. (B) $v = \frac{k}{m} R$
3. (C) $L = mk R^{2}$
4. (D) $L = \frac{mk}{2} R^{2}$
Show answerAnswer
$Answer: options B and C$
Question 5 · JEE Advanced 2016 · one or more correct
The position vector $r$ of a particle of mass m is given by the following equation $ $r (t) = α t^{3} i + β t^{2} j,$ $where $α = \frac{10}{3} m s^{- 3}$ , $β = 5 m s^{- 2}$ and m = 0.1 kg. At t = 1 s, which of the following statement(s) is(are) true about the particle?
1. (A) $The velocity v is given by v = (10 i + 10 j) ms -1$
2. (B) $The angular momentum L with respect to the origin is given by L = - (\frac{5}{3}) k N m s$
3. (C) $The force F is given by F = (i + 2 j) N$
4. (D) $The torque τ with respect to the origin is given by τ = - (\frac{20}{3}) k N m$
Show answerAnswer
$Answer: options A and B and D$

Rotational Motion questions by year

Year	Questions	Share of chapter questions
2026	5
2025	1
2024	2
2023	4
2022	4
2021	2
2020	2
2019	1
2018	4
2017	6
2016	5

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FAQs

How many JEE Advanced questions have been asked from Rotational Motion?

EByAi's bank holds 36 real JEE Advanced questions from Rotational Motion, asked between 2016 and 2026 — about 3 per year on average. Every count is measured from actual papers, not estimated.

Is Rotational Motion important for JEE Advanced?

36 questions over 11 papers make Rotational Motion a steady-weightage chapter in JEE Advanced Physics. The year-wise table above shows exactly how often it appears.

Can I solve Rotational Motion PYQs online for free?

Yes. EByAi lets you solve JEE Advanced past-year questions in the browser with written solutions — free daily practice, no card needed.

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