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

2025 26 questions

1. Q362025 · 8 Apr 2025 · Shift 2

   A rod of linear mass density '$\lambda$' and length 'L' is bent to form a ring of radius 'R'. Moment of inertia of ring about any of its diameter is.

   1. A.$\frac{\lambda L^3}{8{\pi }^2}$
   2. B.$\frac{\lambda L^3}{16{\pi }^2}$
   3. C.$\frac{\lambda L^3}{4{\pi }^2}$
   4. D.$\frac{\lambda L^3}{12}$
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   Answer: A

2. Q472025 · 8 Apr 2025 · Shift 2· Numerical answer

   A thin solid disk of $1\mathrm{kg}$ is rotating along its diameter axis at the speed of $1800\mathrm{rpm}$. By applying an external torque of $25\pi \mathrm{Nm}$ for $40\mathrm{s}$, the speed increases to $2100\mathrm{rpm}$. The diameter of the disk is $\underline{}\mathrm{m}$.

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   Answer: 40

3. Q502025 · 8 Apr 2025 · Shift 2· Numerical answer

   A cube having a side of $10\mathrm{cm}$ with unknown mass and $200\mathrm{gm}$ mass were hung at two ends of a uniform rigid rod of $27\mathrm{cm}$ long. The rod along with masses was placed on a wedge keeping the distance between wedge point and $200\mathrm{gm}$ weight as $25\mathrm{cm}$. Initially the masses were not at balance. A beaker is placed beneath the unknown mass and water is added slowly to it. At given point the masses were in balance and half volume of the unknown mass was inside the water. (Take the density of unknown mass is more than that of the water, the mass did not absorb water and water density is $1{gm/cm}^3$.) The unknown mass is $\underline{}\mathrm{kg}$.

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   Answer: 3

4. Q332025 · 4 Apr 2025 · Shift 1

   Which of the following are correct expression for torque acting on a body? A. $\vec{\tau }=\vec{r}\times \vec{L}$ B. $\vec{\tau }=\frac{d}{dt}(\vec{r}\times \vec{p})$ C. $\vec{\tau }=\vec{r}\times \frac{d\vec{p}}{dt}$ D. $\vec{\tau }=I\vec{\alpha }$ E. $\vec{\tau }=\vec{r}\times \vec{F}$ ($\vec{r}=\text{position vector}$; $\vec{p}=\text{linear momentum}$; $\vec{L}=\text{angular momentum}$; $\vec{\alpha }=\text{angular acceleration}$; $I=\text{moment of inertia}$; $\vec{F}=\text{force}$; $t=\text{time}$) Choose the correct answer from the options given below:

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

5. Q432025 · 4 Apr 2025 · Shift 1

   If $\vec{L}$ and $\vec{P}$ represent the angular momentum and linear momentum respectively of a particle of mass ' $m$ ' having position vector as $\vec{r}=a(\hat{i}\cos \omega t+\hat{j}\sin \omega t)$. The direction of force is

   1. A.Opposite to the direction of $\vec{L}$
   2. B.Opposite to the direction of $\vec{L}\times \vec{P}$
   3. C.Opposite to the direction of $\vec{r}$
   4. D.Opposite to the direction of $\vec{P}$
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   Answer: C

6. Q302025 · 4 Apr 2025 · Shift 2

   A wheel is rolling on a plane surface. The speed of a particle on the highest point of the rim is $8m/s$. The speed of the particle on the rim of the wheel at the same level as the centre of wheel, will be :

   1. A.$4\sqrt{2}m/s$
   2. B.$8m/s$
   3. C.$4m/s$
   4. D.$8\sqrt{2}m/s$
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   Answer: A

7. Q352025 · 4 Apr 2025 · Shift 2

   A cylindrical rod of length $1\mathrm{m}$ and radius $4\mathrm{cm}$ is mounted vertically. It is subjected to a shear force of $10^5\mathrm{N}$ at the top. Considering infinitesimally small displacement in the upper edge, the angular displacement $\theta$ of the rod axis from its original position would be : (shear moduli, $G=10^{10}N/{\mathrm{m}}^2$ )

   1. A.$1/160\pi$
   2. B.$1/2\pi$
   3. C.$1/4\pi$
   4. D.$1/40\pi$
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   Answer: A

8. Q462025 · 4 Apr 2025 · Shift 2· Numerical answer

   A solid sphere with uniform density and radius $R$ is rotating initially with constant angular velocity $({\omega }_1)$ about its diameter. After some time during the rotation it starts losing mass at a uniform rate, with no change in its shape. The angular velocity of the sphere when its radius become $\mathrm{R}/2$ is $x{\omega }_1$. The value of $x$ is ____ .

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   Answer: 32

9. Q302025 · 2 Apr 2025 · Shift 1

   Moment of inertia of a rod of mass ' M ' and length ' L ' about an axis passing through its center and normal to its length is ' $\alpha$ '. Now the rod is cut into two equal parts and these parts are joined symmetrically to form a cross shape. Moment of inertia of cross about an axis passing through its center and normal to plane containing cross is :

   1. A.$\alpha /4$
   2. B.$\alpha /8$
   3. C.$\alpha$
   4. D.$\alpha /2$
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   Answer: A

10. Q322025 · 2 Apr 2025 · Shift 1

    A light wave is propagating with plane wave fronts of the type $x+y+z=\text{constant}$. The angle made by the direction of wave propagation with the $x$-axis is :

    1. A.${\cos }^{-1}(2/3)$
    2. B.${\cos }^{-1}\left(\frac{1}{\sqrt{3}}\right)$
    3. C.${\cos }^{-1}\left(\frac{1}{3}\right)$
    4. D.${\cos }^{-1}\left(\sqrt{\frac{2}{3}}\right)$
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    Answer: B

11. Q442025 · 2 Apr 2025 · Shift 1
    
    1. A.20 rad/s
    2. B.30 rad/s
    3. C.10 rad/s
    4. D.0 rad/s
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    Answer: A

12. Q262025 · 2 Apr 2025 · Shift 2

    The moment of inertia of a circular ring of mass M and diameter r about a tangential axis lying in the plane of the ring is :

    1. A.$\frac{3}{8}\mathrm{M}{\mathrm{r}}^2$
    2. B.$2\mathrm{M}{\mathrm{r}}^2$
    3. C.$\frac{1}{2}\mathrm{M}{\mathrm{r}}^2$
    4. D.$\frac{3}{2}\mathrm{M}{\mathrm{r}}^2$
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    Answer: A

13. Q482025 · 2 Apr 2025 · Shift 2· Numerical answer
    
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    Answer: 1

14. Q262025 · 29 Jan 2025 · Shift 2
    
    1. A.$\frac{1}{2}\mathrm{a}\mathrm{m}{\mathrm{V}}_0$
    2. B.$3\mathrm{a}\mathrm{m}{\mathrm{V}}_0$
    3. C.$\frac{3}{2}\mathrm{a}\mathrm{m}{\mathrm{V}}_0$
    4. D.$\frac{\sqrt{3}}{2}\mathrm{a}\mathrm{m}{\mathrm{V}}_0$
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    Answer: D

15. Q362025 · 29 Jan 2025 · Shift 2

    Match List - I with List - II. $$\begin{array}{ll}\text{List - I}& \text{List - II}\\ \text{(A) Young’s Modulus}& \text{(I) }\mathrm{M}{\mathrm{L}}^{-1}{\mathrm{T}}^{-1}\\ \text{(B) Torque}& \text{(II) }\mathrm{M}{\mathrm{L}}^{-1}{\mathrm{T}}^{-2}\\ \text{(C) Coefficient of Viscosity}& \text{(III) }{\mathrm{M}}^{-1}{\mathrm{L}}^3{\mathrm{T}}^{-2}\\ \text{(D) Gravitational Constant}& \text{(IV) }\mathrm{M}{\mathrm{L}}^2{\mathrm{T}}^{-2}\end{array}$$ Choose the correct answer from the options given below :

    1. A.(A)-(I), (B)-(III), (C)-(II), (D)-(IV)
    2. B.(A)-(IV), (B)-(II), (C)-(III), (D)-(I)
    3. C.(A)-(II), (B)-(I), (C)-(IV), (D)-(III)
    4. D.(A)-(II), (B)-(IV), (C)-(I), (D)-(III)
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    Answer: D

16. Q482025 · 29 Jan 2025 · Shift 2· Numerical answer

    Two planets, $A$ and $B$ are orbiting a common star in circular orbits of radii $R_A$ and $R_B$, respectively, with $R_B=2R_A$. The planet $B$ is $4\sqrt{2}$ times more massive than planet $A$. The ratio $\left(\frac{L_B}{L_A}\right)$ of angular momentum $(L_B)$ of planet $B$ to that of planet $A(L_A)$ is closest to integer ____.

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    Answer: 8

17. Q292025 · 28 Jan 2025 · Shift 1
    
    1. A.$\left(\frac{2}{3}a,\frac{2}{3}b\right)$
    2. B.$\left(\frac{2}{3}a,\frac{b}{2}\right)$
    3. C.$\left(\frac{1}{3}a,\frac{b}{2}\right)$
    4. D.$\left(\frac{a}{2},\frac{b}{2}\right)$
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    Answer: B

18. Q462025 · 28 Jan 2025 · Shift 1· Numerical answer

    Two iron solid discs of negligible thickness have radii $R_1$ and $R_2$ and moment of inertia $I_1$ and $I_2$, respectively. For $R_2=2R_1$, the ratio of $I_1$ and $I_2$ would be $1/x$, where $x=$ ____ .

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    Answer: 16

19. Q482025 · 28 Jan 2025 · Shift 1· Numerical answer

    The moment of inertia of a solid disc rotating along its diameter is $2.5$ times higher than the moment of inertia of a ring rotating in similar way. The moment of inertia of a solid sphere which has same radius as the disc and rotating in similar way, is $n$ times higher than the moment of inertia of the given ring. Here, $n=$ ____ Consider all the bodies have equal masses.

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    Answer: 4

20. Q262025 · 24 Jan 2025 · Shift 1

    An object of mass ' m ' is projected from origin in a vertical xy plane at an angle $45^{\circ }$ with the $x-$ axis with an initial velocity $v_0$. The magnitude and direction of the angular momentum of the object with respect to origin, when it reaches at the maximum height, will be [ g is acceleration due to gravity]

    1. A.$\frac{m{v}_0^3}{2\sqrt{2}g}$ along negative $z$-axis
    2. B.$\frac{m{v}_0^3}{2\sqrt{2}g}$ along positive $z$-axis
    3. C.$\frac{m{v}_0^3}{4\sqrt{2}g}$ along positive $z$-axis
    4. D.$\frac{m{v}_0^3}{4\sqrt{2}g}$ along negative $z$-axis
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    Answer: D

21. Q432025 · 24 Jan 2025 · Shift 1

    A uniform solid cylinder of mass ' m ' and radius ' r ' rolls along an inclined rough plane of inclination $45^{\circ }$. If it starts to roll from rest from the top of the plane then the linear acceleration of the cylinder's axis will be

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

22. Q262025 · 24 Jan 2025 · Shift 2
    
    1. A.$\frac{{\mathrm{N}}^2}{2\pi }q\omega$
    2. B.$\frac{\mathrm{N}}{2\pi }q\omega$
    3. C.$\frac{2\pi }{\mathrm{N}}q\omega$
    4. D.$\frac{\mathrm{N}}{\pi }q\omega$
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    Answer: B

23. Q412025 · 24 Jan 2025 · Shift 2

    A solid sphere is rolling without slipping on a horizontal plane. The ratio of the linear kinetic energy of the centre of mass of the sphere and rotational kinetic energy is :

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

24. Q442025 · 23 Jan 2025 · Shift 2

    A circular disk of radius R meter and mass M kg is rotating around the axis perpendicular to the disk. An external torque is applied to the disk such that $\theta (t)=5t^2-8t$, where $\theta (t)$ is the angular position of the rotating disc as a function of time $t$. How much power is delivered by the applied torque, when $t=2\text{ s}$ ?

    1. A.$60{\mathrm{MR}}^2$
    2. B.$72{\mathrm{MR}}^2$
    3. C.$8{\mathrm{MR}}^2$
    4. D.$108{\mathrm{MR}}^2$
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    Answer: A

25. Q282025 · 22 Jan 2025 · Shift 1
    
    1. A.$\frac{17}{32}{\mathrm{MR}}^2$
    2. B.$\frac{13}{32}{\mathrm{MR}}^2$
    3. C.$\frac{9}{32}{\mathrm{MR}}^2$
    4. D.$\frac{7}{32}{\mathrm{MR}}^2$
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    Answer: B