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

2024 28 questions

1. Q582024 · 9 Apr 2024 · Shift 1· Numerical answer

   A string is wrapped around the rim of a wheel of moment of inertia $0.40{\text{ kgm}}^2$ and radius $10\text{ cm}$. The wheel is free to rotate about its axis. Initially the wheel is at rest. The string is now pulled by a force of $40\text{ N}$. The angular velocity of the wheel after $10\text{ s}$ is $x\text{ rad/s}$, where $x$ is ______.

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   Answer: 100

2. Q492024 · 9 Apr 2024 · Shift 2
   
   1. A.$1\mathrm{N}$
   2. B.$10\mathrm{N}$
   3. C.$\frac{10}{\sqrt{2}}N$
   4. D.$\frac{1}{10\times \sqrt{2}}N$
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   Answer: B

3. Q332024 · 8 Apr 2024 · Shift 1

   Two planets $A$ and $B$ having masses $m_1$ and $m_2$ move around the sun in circular orbits of $r_1$ and $r_2$ radii respectively. If angular momentum of $A$ is $L$ and that of $B$ is $3L$, the ratio of time period $\left(\frac{T_A}{T_B}\right)$ is:

   1. A.${\left(\frac{r_2}{r_1}\right)}^{\frac{3}{2}}$
   2. B.$27{\left(\frac{m_1}{m_2}\right)}^3$
   3. C.${\left(\frac{r_1}{r_2}\right)}^3$
   4. D.$\frac{1}{27}{\left(\frac{m_2}{m_1}\right)}^3$
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   Answer: D

4. Q482024 · 8 Apr 2024 · Shift 2

   A thin circular disc of mass $\mathrm{M}$ and radius $\mathrm{R}$ is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity $\omega$. If another disc of same dimensions but of mass $\mathrm{M}/2$ is placed gently on the first disc co-axially, then the new angular velocity of the system is :

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

5. Q562024 · 8 Apr 2024 · Shift 2· Numerical answer
   
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   Answer: 2

6. Q522024 · 6 Apr 2024 · Shift 2· Numerical answer

   Three balls of masses $2\text{ kg}$, $4\text{ kg}$ and $6\text{ kg}$ respectively are arranged at centre of the edges of an equilateral triangle of side $2\text{ m}$. The moment of inertia of the system about an axis through the centroid and perpendicular to the plane of triangle, will be ________ ${\text{kg m}}^2$.

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   Answer: 4

7. Q462024 · 5 Apr 2024 · Shift 2

   The angular momentum of an electron in a hydrogen atom is proportional to : (Where $r$ is the radius of orbit of electron)

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

8. Q542024 · 5 Apr 2024 · Shift 2· Numerical answer

   A hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is $\frac{x}{5}$. The value of $x$ is ____.

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   Answer: 2

9. Q512024 · 4 Apr 2024 · Shift 2· Numerical answer

   In a system two particles of masses $m_1=3\text{ kg}$ and $m_2=2\text{ kg}$ are placed at certain distance from each other. The particle of mass $m_1$ is moved towards the center of mass of the system through a distance $2\text{ cm}$. In order to keep the center of mass of the system at the original position, the particle of mass $m_2$ should move towards the center of mass by the distance ________ $\text{cm}$.

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   Answer: 3

10. Q542024 · 4 Apr 2024 · Shift 2· Numerical answer

    A rod of length $60\text{ cm}$ rotates with a uniform angular velocity $20\text{ rad}{\text{s}}^{-1}$ about its perpendicular bisector, in a uniform magnetic field $0.5T$. The direction of magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is ________ V.

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    Answer: 0

11. Q372024 · 1 Feb 2024 · Shift 1

    A ball of mass $0.5\mathrm{kg}$ is attached to a string of length $50\mathrm{cm}$. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is $400\mathrm{N}$. The maximum possible value of angular velocity of the ball in $rad/s$ is :

    1. A.1600
    2. B.20
    3. C.40
    4. D.1000
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    Answer: C

12. Q582024 · 1 Feb 2024 · Shift 1· Numerical answer

    Three identical spheres each of mass $2\mathrm{M}$ are placed at the corners of a right angled triangle with mutually perpendicular sides equal to $4\mathrm{m}$ each. Taking point of intersection of these two sides as origin, the magnitude of position vector of the centre of mass of the system is $\frac{4\sqrt{2}}{x}$, where the value of $x$ is ____ .

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    Answer: 3

13. Q502024 · 1 Feb 2024 · Shift 2
    
    1. A.$\frac{3}{4}\frac{v^2}{g}$
    2. B.$\frac{v^2}{g}$
    3. C.$\frac{2}{3}\frac{v^2}{g}$
    4. D.$\frac{1}{2}\frac{v^2}{g}$
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    Answer: D

14. Q532024 · 1 Feb 2024 · Shift 2· Numerical answer

    A particle initially at rest starts moving from reference point $x=0$ along $x$-axis, with velocity $v$ that varies as $v=4\sqrt{x}\text{ m/s}$. The acceleration of the particle is ________ $\mathrm{m}{\mathrm{s}}^{-2}$.

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    Answer: 8

15. Q592024 · 1 Feb 2024 · Shift 2· Numerical answer

    A uniform rod $AB$ of mass $2\text{ kg}$ and length $30\text{ cm}$ is at rest on a smooth horizontal surface. An impulse of force $0.2\text{ Ns}$ is applied to end B. The time taken by the rod to turn through at right angles will be $\frac{\pi }{x}\text{ s}$, where $x=$ ________ .

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    Answer: 4

16. Q442024 · 31 Jan 2024 · Shift 1

    A coin is placed on a disc. The coefficient of friction between the coin and the disc is $\mu$. If the distance of the coin from the center of the disc is $r$, the maximum angular velocity which can be given to the disc, so that the coin does not slip away, is :

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

17. Q512024 · 31 Jan 2024 · Shift 1· Numerical answer

    A solid circular disc of mass $50\mathrm{kg}$ rolls along a horizontal floor so that its center of mass has a speed of $0.4m/s$. The absolute value of work done on the disc to stop it is ____ J.

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    Answer: 6

18. Q352024 · 31 Jan 2024 · Shift 2

    A uniform magnetic field of $2\times 10^{-3}\mathrm{T}$ acts along positive $Y$-direction. A rectangular loop of sides $20\mathrm{cm}$ and $10\mathrm{cm}$ with current of $5\mathrm{A}$ is in $Y-Z$ plane. The current is in anticlockwise sense with reference to negative $X$ axis. Magnitude and direction of the torque is:

    1. A.$2\times 10^{-4}\mathrm{N}\text{-}\mathrm{m}$ along negative $Z$-direction
    2. B.$2\times 10^{-4}\mathrm{N}\text{-}\mathrm{m}$ along positive $X$-direction
    3. C.$2\times 10^{-4}\mathrm{N}\text{-}\mathrm{m}$ along positive $Y$-direction
    4. D.$2\times 10^{-4}\mathrm{N}\text{-}\mathrm{m}$ along positive $Z$-direction
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    Answer: A

19. Q522024 · 31 Jan 2024 · Shift 2· Numerical answer

    A body of mass '$m$' is projected with a speed '$u$' making an angle of $45^{\circ }$ with the ground. The angular momentum of the body about the point of projection, at the highest point is expressed as $\frac{\sqrt{2}m{u}^3}{Xg}$. The value of '$X$' is ____.

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    Answer: 8

20. Q552024 · 31 Jan 2024 · Shift 2· Numerical answer

    Two identical spheres each of mass $2\mathrm{kg}$ and radius $50\mathrm{cm}$ are fixed at the ends of a light rod so that the separation between the centers is $150\mathrm{cm}$. Then, moment of inertia of the system about an axis perpendicular to the rod and passing through its middle point is $\frac{x}{20}\mathrm{kg}{\mathrm{m}}^2$, where the value of $x$ is ____.

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    Answer: 53

21. Q342024 · 30 Jan 2024 · Shift 1

    A particle of mass $\mathrm{m}$ is projected with a velocity '$\mathrm{u}$' making an angle of $30^{\circ }$ with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height $\mathrm{h}$ is :

    1. A.$\frac{{\mathrm{mu}}^3}{\sqrt{2}\mathrm{g}}$
    2. B.zero
    3. C.$\frac{\sqrt{3}}{2}\frac{{\mathrm{mu}}^2}{\mathrm{g}}$
    4. D.$\frac{\sqrt{3}}{16}\frac{{\mathrm{mu}}^3}{\mathrm{g}}$
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    Answer: D

22. Q422024 · 30 Jan 2024 · Shift 1

    Match List I with List II. | | List I | | List II | |---|---|---|---| | (A) | Coefficient of viscosity | (I) | $[\mathrm{M}{\mathrm{L}}^2{\mathrm{T}}^{-2}]$ | | (B) | Surface tension | (II) | $[\mathrm{M}{\mathrm{L}}^2{\mathrm{T}}^{-1}]$ | | (C) | Angular momentum | (III) | $[\mathrm{M}{\mathrm{L}}^{-1}{\mathrm{T}}^{-1}]$ | | (D) | Rotational kinetic energy | (IV) | $[\mathrm{M}{\mathrm{L}}^0{\mathrm{T}}^{-2}]$ | Choose the correct answer from the options given below :

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

23. Q572024 · 30 Jan 2024 · Shift 1· Numerical answer
    
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    Answer: 250

24. Q522024 · 29 Jan 2024 · Shift 1· Numerical answer

    A cylinder is rolling down on an inclined plane of inclination $60^{\circ }$. Its acceleration during rolling down will be $\frac{x}{\sqrt{3}}{\text{m/s}}^2$, where $x=$ _______ (use $\text{g}=10{\text{ m/s}}^2$).

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    Answer: 10

25. Q542024 · 29 Jan 2024 · Shift 2· Numerical answer

    A body of mass $5\text{ kg}$ moving with a uniform speed $3\sqrt{2}{\text{ ms}}^{-1}$ in $X-Y$ plane along the line $y=x+4$. The angular momentum of the particle about the origin will be _________ $\mathrm{kg}{\mathrm{m}}^2{\mathrm{s}}^{-1}$.

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    Answer: 60