Centre of Mass & Rotational Motion · JEE Main previous year questions

2026 33 questions

1. Q322026 · 8 Apr 2026 · Shift 2

   A set of four observations has mean 1 and variance 13. Another set of six observations has mean 2 and variance 1 . Then, the variance of all these 10 observations is equal to :

   1. A.5.96
   2. B.6.14
   3. C.6.04
   4. D.6.24
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   Answer: B

2. Q352026 · 8 Apr 2026 · Shift 2

   One mole of diatomic gas having rotational modes only is kept in a cylinder with a piston system. The cross-section area of the cylinder is $4\mathrm{c}{\mathrm{m}}^2$. The gas is heated slowly to raise the temperature by $1.2{}^{\circ }\mathrm{C}$ during which the piston moves by $25\mathrm{mm}$. The amount of heat supplied to the gas is ____ $\mathrm{J}$. (Atmospheric pressure $=100\mathrm{kPa}$, $R=8.3J/mol\cdot \mathrm{K}$) (Neglect mass of the piston)

   1. A.$24.8$
   2. B.$25$
   3. C.$15.04$
   4. D.$29.98$
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   Answer: A, B

3. Q392026 · 8 Apr 2026 · Shift 2

   A current carrying circular loop of radius $2\mathrm{cm}$ with unit normal $\hat{n}=\frac{\hat{k}+\hat{i}}{\sqrt{2}}$ is placed in a magnetic field, $\vec{B}=B_0\left(3\hat{i}+2\hat{k}\right)$. If $B_0=4\times 10^{-3}\mathrm{T}$ and current $I=100\sqrt{2}\mathrm{A}$, the torque experienced by the loop is ____ $Wb.A$. $(\pi =3.14)$

   1. A.$16\times 10^{-5}\hat{k}$
   2. B.$5024\times 10^{-7}\hat{k}$
   3. C.$5024\times 10^{-7}\hat{i}$
   4. D.$5024\times 10^{-7}\hat{j}$
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   Answer: D

4. Q312026 · 6 Apr 2026 · Shift 1

   A solid sphere of radius $4\mathrm{cm}$ and mass $5\mathrm{kg}$ is rotating (rotation axis is passing through the centre of the sphere) with an angular velocity of $1200\mathrm{rpm}$. It is brought to rest in $10\mathrm{s}$ by applying a constant torque. The torque applied and the number of rotations it made before it comes to rest are ____ and ____ respectively.

   1. A.$0.128\pi \mathrm{Nm}$, 100
   2. B.$0.0128\pi \mathrm{Nm}$, 50
   3. C.$0.128\pi \mathrm{Nm}$, 50
   4. D.$0.0128\pi \mathrm{Nm}$, 100
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   Answer: D

5. Q332026 · 6 Apr 2026 · Shift 1
   
   1. A.$\left(\frac{\sqrt{3}}{4},1.25\right)$
   2. B.$\left(\frac{\sqrt{3}}{4},1.0\right)$
   3. C.$(0,0)$
   4. D.$(1.25,0)$
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   Answer: A

6. Q282026 · 6 Apr 2026 · Shift 2

   A solid sphere $(A)$ of mass $5m$ and a spherical shell $(B)$ of mass $m$, both having same radius, are placed on a rough surface. When a force of same magnitude is applied tangentially at the highest points of $A$ and $B$, they start rolling without slipping with an acceleration of $a_A$ and $a_B$, respectively. The ratio of $a_A$ and $a_B$ is ____ .

   1. A.$5:21$
   2. B.$6:10$
   3. C.$21:25$
   4. D.$1:5$
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   Answer: A

7. Q302026 · 5 Apr 2026 · Shift 2

   A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first $2\mathrm{s}$ it rotates through an angle ${\theta }_1$ and in the next $2\mathrm{s}$ it rotates through an angle ${\theta }_2$. The ratio $\frac{{\theta }_2}{{\theta }_1}$ is ____.

   1. A.6
   2. B.3
   3. C.4
   4. D.$\frac{1}{3}$
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   Answer: B

8. Q362026 · 5 Apr 2026 · Shift 2

   A metal rod of length $L$ rotates about one end at origin with a uniform angular velocity $\omega$. The magnetic field radially falls off as $B(r)=B_{\circ }{\mathrm{e}}^{-\lambda r}$; $\lambda$ being a positive constant. The emf induced (neglecting the centripetal force on electrons in the rod) is :

   1. A.$B_{\circ }\omega \left[\frac{1}{{\lambda }^2}-{\mathrm{e}}^{-\lambda L}\left(\frac{1}{{\lambda }^2}+\frac{L}{\lambda }\right)\right]$
   2. B.$B_{\circ }\omega \left[\frac{1}{{\lambda }^2}+{\mathrm{e}}^{-\lambda L}\left(\frac{1}{{\lambda }^2}+\frac{L}{\lambda }\right)\right]$
   3. C.$B_{\circ }\omega \left[\frac{4}{{\lambda }^2}-{\mathrm{e}}^{-2\lambda L}\left(\frac{1}{{\lambda }^2}+\frac{2L}{\lambda }\right)\right]$
   4. D.$B_{\circ }\omega \left[\frac{3}{{\lambda }^2}-{\mathrm{e}}^{-3\lambda L}\left(\frac{3}{{\lambda }^2}+\frac{L}{\lambda }\right)\right]$
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   Answer: A

9. Q302026 · 4 Apr 2026 · Shift 1

   A solid sphere of mass $M$ and radius $R$ is divided into two unequal parts. The smaller part having mass $M/8$ is converted into a sphere of radius $r$ and the larger part is converted into a circular disc of thickness $t$ and radius $2R$. If $I_1$ is moment of inertia of a sphere having radius $r$ about an axis through its centre and $I_2$ is the moment of inertia of a disc about its diameter, the ratio of their moment of inertia $I_2/I_1=$ _________.

   1. A.35
   2. B.70
   3. C.140
   4. D.210
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   Answer: B

10. Q492026 · 4 Apr 2026 · Shift 1· Numerical answer

    A body of mass $2\text{ kg}$ begins to move under the influence of time dependent force $\vec{F}=(2t\hat{i}+6t^2\hat{j})\text{ N}$, where $\hat{i}$ and $\hat{j}$ are unit vectors along $x$ and $y$-axis respectively. The power produced by the force at $t=2\text{ s}$ is ________ $\text{W}$.

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    Answer: 200

11. Q352026 · 4 Apr 2026 · Shift 2
    
    1. A.$2\pi \sqrt{\frac{5R}{4g}}$
    2. B.$2\pi \sqrt{\frac{2R}{3g}}$
    3. C.$2\pi \sqrt{\frac{3R}{2g}}$
    4. D.$2\pi \sqrt{\frac{3R}{g}}$
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    Answer: A

12. Q492026 · 4 Apr 2026 · Shift 2· Numerical answer

    A circular coil of radius $2\mathrm{cm}$ and $125$ turns carries a current of $1\mathrm{A}$. The coil is placed in a uniform magnetic field of magnitude $0.4\mathrm{T}$. The axis of the coil makes an angle of $30^{\circ }$ with the direction of the magnetic field. The torque acting on the coil is $\alpha \times 10^{-4}N.m$. The value of $\alpha$ is ____. ($\pi =3.14$)

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    Answer: 314

13. Q292026 · 2 Apr 2026 · Shift 1

    The position of an object having mass $0.1\mathrm{kg}$ as a function of time $t$ is given as $\vec{r}=\left(10t^2\hat{i}+5t^3\hat{j}\right)\mathrm{m}$. At $t=1\mathrm{s}$, which of the following statements are correct ? A. The linear momentum $\vec{p}=\left(2\hat{i}+1.5\hat{j}\right)\mathrm{kg}\cdot \mathrm{m}/\mathrm{s}$. B. The force acting on the object $\vec{\mathrm{F}}=\left(2\hat{i}+3\hat{j}\right)\mathrm{N}$. C. The angular momentum of the object about its origin $\vec{\mathrm{L}}=15\hat{\mathrm{k}}\mathrm{J}\mathrm{s}$. D. The torque acting on the object about its origin $\vec{\tau }=20\hat{\mathrm{k}}\mathrm{N}\mathrm{m}$. Choose the correct answer from the options given below :

    1. A.A, B and C only
    2. B.B, C and D only
    3. C.A, C and D only
    4. D.A, B and D only
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    Answer: D

14. Q312026 · 2 Apr 2026 · Shift 1

    The number of seven-digit numbers, that can be formed by using the digits 1, 2, 3, 5 and 7 such that each digit is used at least once, is:

    1. A.15400
    2. B.17800
    3. C.16800
    4. D.29400
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    Answer: C

15. Q442026 · 2 Apr 2026 · Shift 1

    Angular momentum of an electron in a hydrogen atom is $\frac{3h}{\pi }$, then the energy of the electron is ____ $\mathrm{eV}$.

    1. A.-1.51
    2. B.-0.85
    3. C.-0.38
    4. D.-0.28
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    Answer: C

16. Q272026 · 2 Apr 2026 · Shift 2

    A $0.5\mathrm{kg}$ mass is in contact against the inner wall of a cylindrical drum of radius $4\mathrm{m}$ rotating about its vertical axis. The minimum rotational speed of the drum to enable the mass to remain stuck to the wall (without falling) is $5rad/s$. The coefficient of friction between the drum's inner wall surface and mass is ____. (Take $g=10m/{\mathrm{s}}^2$)

    1. A.$0.1$
    2. B.$0.5$
    3. C.$0.7$
    4. D.$0.3$
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    Answer: A

17. Q502026 · 2 Apr 2026 · Shift 2· Numerical answer
    
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    Answer: 60

18. Q262026 · 28 Jan 2026 · Shift 1
    
    1. A.100
    2. B.22
    3. C.27
    4. D.11
    Show answer

    Answer: D

19. Q462026 · 28 Jan 2026 · Shift 1· Numerical answer

    A solid sphere of radius $10\mathrm{cm}$ is rotating about an axis which is at a distance $15\mathrm{cm}$ from its centre. The radius of gyration about this axis is $\sqrt{n}\mathrm{cm}$. The value of $n$ is

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    Answer: 265

20. Q492026 · 28 Jan 2026 · Shift 2· Numerical answer

    A fly wheel having mass 3 kg and radius 5 m is free to rotate about a horizontal axis. A string having negligible mass is wound around the wheel and the loose end of the string is connected to 3 kg mass. The mass is kept at rest initially and released. Kinetic energy of the wheel when the mass descends by 3 m is ________ J. $(g=10{\text{ m/s}}^2)$

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    Answer: 30

21. Q472026 · 24 Jan 2026 · Shift 1· Numerical answer

    A short bar magnet placed with its axis at $30^{\circ }$ with an external field of $800\mathrm{Gauss}$, experiences a torque of $0.016\mathrm{N}\cdot \mathrm{m}$. The work done in moving it from most stable to most unstable position is $\alpha \times 10^{-3}\mathrm{J}$. The value of $\alpha$ is ____ .

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    Answer: 64

22. Q502026 · 24 Jan 2026 · Shift 1· Numerical answer

    A gas of certain mass filled in a closed cylinder at a pressure of $3.23\mathrm{kPa}$ has temperature $50^{\circ }\mathrm{C}$. The gas is now heated to double its temperature. The modified pressure is ____ $\mathrm{Pa}$ .

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    Answer: 3730 or 6460

23. Q322026 · 23 Jan 2026 · Shift 1

    Two small balls with masses $m$ and $2m$ are attached to both ends of a rigid rod of length $d$ and negligible mass. If angular momentum of this system is $L$ about an axis (A) passing through its centre of mass and perpendicular to the rod then angular velocity of the system about $A$ is :

    1. A.$\frac{4}{3}\frac{L}{m{d}^2}$
    2. B.$\frac{3}{2}\frac{L}{m{d}^2}$
    3. C.$\frac{2L}{5m{d}^2}$
    4. D.$\frac{2L}{m{d}^2}$
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    Answer: B

24. Q372026 · 23 Jan 2026 · Shift 1

    The moment of inertia of a square loop made of four uniform solid cylinders, each having radius $R$ and length $L(\mathrm{R}<\mathrm{L})$ about an axis passing through the mid points of opposite sides, is (Take the mass of the entire loop as $M$ ) :

    1. A.$\frac{3}{4}M{R}^2+\frac{1}{6}M{L}^2$
    2. B.$\frac{3}{8}M{R}^2+\frac{7}{12}M{L}^2$
    3. C.$\frac{3}{4}M{R}^2+\frac{7}{12}M{L}^2$
    4. D.$\frac{3}{8}M{R}^2+\frac{1}{6}M{L}^2$
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    Answer: D

25. Q492026 · 23 Jan 2026 · Shift 2· Numerical answer
    
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    Answer: 109