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JEE Advanced System of Particles and Rotational Motion — practice questions

Explore 34 free System of Particles and Rotational Motion questions in JEE Advanced Physics. Open each question or exercise to read its content, reference answers and available explanation.

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System of Particles and Rotational Motion questions and exercises with answers

Showing questions 1–30 of 34.

The moment of inertia of a solid sphere of mass $M$ and radius $R$ about a diameter is:Read the answer and worked solution →The **moment of inertia** of a thin uniform rod of mass $M$ and length $L$ about a perpendicular axis through its **centre** is:Read the answer and worked solution →The **angular momentum** of a particle of momentum $\vec p$ at position $\vec r$ (from origin) is:Read the answer and worked solution →For a body **rolling without slipping** on a flat surface with centre-of-mass velocity $v$, the **velocity of the topmost point** is:Read the answer and worked solution →A solid sphere ($I = \tfrac{2}{5}MR^2$) rolls without slipping down a plane inclined at $\theta$. Its **linear acceleration** is:Read the answer and worked solution →By **parallel-axis theorem**, the moment of inertia of a thin ring of mass $M$, radius $R$, about a tangent in its plane is:Read the answer and worked solution →A uniform rod of length $L$ is suspended from one end. Its **time period** for small oscillations is:Read the answer and worked solution →A **yo-yo** (solid uniform cylinder) of mass $M$, radius $R$ unwinds under gravity. Its downward acceleration is:Read the answer and worked solution →Angular displacement theta in a circular motion is related to arc length s and radius r as:Read the answer and worked solution →Angular velocity omega in terms of time period T:Read the answer and worked solution →What makes a body rigidRead the answer and worked solution →Rigid bodies and their motionRead the answer and worked solution →Rotation about a fixed axisRead the answer and worked solution →Odd one out: rotationRead the answer and worked solution →Angular velocity is a vectorRead the answer and worked solution →Linear velocity in rotationRead the answer and worked solution →The cross productRead the answer and worked solution →Vector operation to resultRead the answer and worked solution →The centre of massRead the answer and worked solution →Momentum of a systemRead the answer and worked solution →Defining the centre of massRead the answer and worked solution →Quantity to definitionRead the answer and worked solution →Torque and its other nameRead the answer and worked solution →Angular momentumRead the answer and worked solution →Odd one out: system quantitiesRead the answer and worked solution →Torque, in wordsRead the answer and worked solution →Which is largerRead the answer and worked solution →Same axis, same omegaRead the answer and worked solution →Translation versus rotationRead the answer and worked solution →Motion to descriptionRead the answer and worked solution →

Worked practice questions

The moment of inertia of a solid sphere of mass $M$ and radius $R$ about a diameter is:

  1. $\dfrac{1}{2}MR^2$
  2. $\dfrac{2}{3}MR^2$
  3. $\dfrac{2}{5}MR^2$
  4. $MR^2$
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Correct answer: C. $\dfrac{2}{5}MR^2$

Standard result for a solid sphere about a central axis: $I = \dfrac{2}{5}MR^2$. Compare with a hollow (thin-shell) sphere where $I = \dfrac{2}{3}MR^2$ — that's option D and a common trap.

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The **moment of inertia** of a thin uniform rod of mass $M$ and length $L$ about a perpendicular axis through its **centre** is:

  1. $ML^2/3$
  2. $ML^2/12$
  3. $ML^2/2$
  4. $ML^2$
Show answer and solution

Correct answer: B. $ML^2/12$

**Standard result:** $I_{\text{cm}} = ML^2/12$. **About one end (parallel axis):** $I = ML^2/12 + M(L/2)^2 = ML^2/3$.

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The **angular momentum** of a particle of momentum $\vec p$ at position $\vec r$ (from origin) is:

  1. $\vec p \cdot \vec r$
  2. $\vec r \times \vec p$
  3. $\vec p \times \vec r$
  4. $|\vec r||\vec p|$ always
Show answer and solution

Correct answer: B. $\vec r \times \vec p$

$\vec L = \vec r \times \vec p$ (right-hand rule). Note $\vec r \times \vec p = -\vec p \times \vec r$, order matters.

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