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

2023 41 questions

1. Q342023 · 13 Apr 2023 · Shift 1
   
   1. A.$27\text{ Pa}$
   2. B.$175\text{ Pa}$
   3. C.$135\text{ Pa}$
   4. D.$36\text{ Pa}$
   Show answer

   Answer: B

2. Q402023 · 13 Apr 2023 · Shift 1
   
   1. A.$R\sqrt{({\pi }^2+1)}$
   2. B.$2R$
   3. C.$R\sqrt{({\pi }^2+4)}$
   4. D.$2R\sqrt{(1+4{\pi }^2)}$
   Show answer

   Answer: C

3. Q582023 · 13 Apr 2023 · Shift 1· Numerical answer

   A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is $\pi :22$ then, the value of its angular speed will be ___________ $\text{rad/s}$.

   Show answer

   Answer: 4

4. Q532023 · 13 Apr 2023 · Shift 2· Numerical answer

   A light rope is wound around a hollow cylinder of mass $5\text{ kg}$ and radius $70\text{ cm}$. The rope is pulled with a force of $52.5\text{ N}$. The angular acceleration of the cylinder will be ___________ ${\text{rad s}}^{-2}$.

   Show answer

   Answer: 15

5. Q332023 · 12 Apr 2023 · Shift 1

   Match List I with List II | LIST I | | LIST II | | :--- | :--- | :--- | | A. Spring constant | I. | $[{\mathrm{T}}^{-1}]$ | | B. Angular speed | II. | $[\mathrm{M}{\mathrm{T}}^{-2}]$ | | C. Angular momentum | III. | $[\mathrm{M}{\mathrm{L}}^2]$ | | D. Moment of inertia | IV. | $[\mathrm{M}{\mathrm{L}}^2{\mathrm{T}}^{-1}]$ | Choose the correct answer from the options given below:

   1. A.A-IV, B-I, C-III, D-II
   2. B.A-II, B-III, C-I, D-IV
   3. C.A-II, B-I, C-IV, D-III
   4. D.A-I, B-III, C-II, D-IV
   Show answer

   Answer: C

6. Q532023 · 12 Apr 2023 · Shift 1· Numerical answer

   For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is $\frac{x}{5}$. The value of $x$ is _________.

   Show answer

   Answer: 2

7. Q382023 · 11 Apr 2023 · Shift 1

   A coin placed on a rotating table just slips when it is placed at a distance of 1 cm from the center. If the angular velocity of the table is halved, it will just slip when placed at a distance of _________ from the centre :

   1. A.1 cm
   2. B.8 cm
   3. C.4 cm
   4. D.2 cm
   Show answer

   Answer: C

8. Q562023 · 11 Apr 2023 · Shift 1· Numerical answer

   A solid sphere of mass $500\text{ g}$ and radius $5\text{ cm}$ is rotated about one of its diameters with angular speed of $10{\text{ rad s}}^{-1}$. If the moment of inertia of the sphere about its tangent is $x\times 10^{-2}$ times its angular momentum about the diameter. Then the value of $x$ will be _________.

   Show answer

   Answer: 35

9. Q522023 · 11 Apr 2023 · Shift 2· Numerical answer

   A circular plate is rotating in horizontal plane, about an axis passing through its center and perpendicular to the plate, with an angular velocity $\omega$. A person sits at the center having two dumbbells in his hands. When he stretches out his hands, the moment of inertia of the system becomes triple. If E be the initial Kinetic energy of the system, then final Kinetic energy will be $\frac{E}{x}$. The value of $x$ is _________.

   Show answer

   Answer: 3

10. Q572023 · 10 Apr 2023 · Shift 1· Numerical answer

    If the earth suddenly shrinks to $\frac{1}{64}\text{th}$ of its original volume with its mass remaining the same, the period of rotation of earth becomes $\frac{24}{x}\text{ h}$. The value of x is _________.

    Show answer

    Answer: 16

11. Q332023 · 10 Apr 2023 · Shift 2

    Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : An electric fan continues to rotate for some time after the current is switched off. Reason R : Fan continues to rotate due to inertia of motion. In the light of above statements, choose the most appropriate answer from the options given below.

    1. A.A is not correct but R is correct
    2. B.A is correct but R is not correct
    3. C.Both A and R are correct and R is the correct explanation of A
    4. D.Both A and R are correct but R is NOT the correct explanation of A
    Show answer

    Answer: C

12. Q362023 · 10 Apr 2023 · Shift 2

    A bar magnet is released from rest along the axis of a very long vertical copper tube. After some time the magnet will

    1. A.move down with almost constant speed
    2. B.move down with an acceleration equal to g
    3. C.move down with an acceleration greater than g
    4. D.oscillate inside the tube
    Show answer

    Answer: A

13. Q462023 · 10 Apr 2023 · Shift 2

    Given below are two statements: Statement I : Rotation of the earth shows effect on the value of acceleration due to gravity (g) Statement II : The effect of rotation of the earth on the value of 'g' at the equator is minimum and that at the pole is maximum. In the light of the above statements, choose the correct answer from the options given below

    1. A.Statement I is false but statement II is true
    2. B.Statement I is true but statement II is false
    3. C.Both Statement I and Statement II are true
    4. D.Both Statement I and Statement II are false
    Show answer

    Answer: B

14. Q512023 · 10 Apr 2023 · Shift 2· Numerical answer

    A force of $-P\hat{k}$ acts on the origin of the coordinate system. The torque about the point $(2,-3)$ is $P(a\hat{i}+b\hat{j})$. The ratio of $\frac{a}{b}$ is $\frac{x}{2}$. The value of $x$ is _________.

    Show answer

    Answer: 3

15. Q602023 · 8 Apr 2023 · Shift 1· Numerical answer

    The moment of inertia of a semicircular ring about an axis, passing through the center and perpendicular to the plane of ring, is $\frac{1}{x}{\mathrm{MR}}^2$, where $\mathrm{R}$ is the radius and $M$ is the mass of the semicircular ring. The value of $x$ will be ___________.

    Show answer

    Answer: 1

16. Q332023 · 8 Apr 2023 · Shift 2
    
    1. A.$x(t)=r\cos \left(\omega t-\frac{\pi }{6}\omega \right)$
    2. B.$x(t)=r\cos (\omega t)$
    3. C.$x(t)=r\cos \left(\omega t+\frac{\pi }{6}\right)$
    4. D.$x(t)=r\sin \left(\omega t+\frac{\pi }{6}\right)$
    Show answer

    Answer: C

17. Q422023 · 8 Apr 2023 · Shift 2

    The orbital angular momentum of a satellite is L, when it is revolving in a circular orbit at height h from earth surface. If the distance of satellite from the earth centre is increased by eight times to its initial value, then the new angular momentum will be -

    1. A.9L
    2. B.8L
    3. C.4L
    4. D.3L
    Show answer

    Answer: D

18. Q462023 · 8 Apr 2023 · Shift 2

    Match List I with List II $$\begin{array}{llll}& \text{LIST I}& & \text{LIST II}\\ \text{A.}& \text{Torque}& \text{I.}& \mathrm{M}{\mathrm{L}}^{-2}{\mathrm{T}}^{-2}\\ \text{B.}& \text{Stress}& \text{II.}& \mathrm{M}{\mathrm{L}}^2{\mathrm{T}}^{-2}\\ \text{C.}& \text{Pressure gradient}& \text{III.}& \mathrm{M}{\mathrm{L}}^{-1}{\mathrm{T}}^{-1}\\ \text{D.}& \text{Coefficient of viscosity}& \text{IV.}& \mathrm{M}{\mathrm{L}}^{-1}{\mathrm{T}}^{-2}\end{array}$$ Choose the correct answer from the options given below:

    1. A.A-II, B-I, C-IV, D-III
    2. B.A-II, B-IV, C-I, D-III
    3. C.A-IV, B-II, C-III, D-I
    4. D.A-III, B-IV, C-I, D-II
    Show answer

    Answer: B

19. Q562023 · 8 Apr 2023 · Shift 2· Numerical answer

    A steel rod of length $1\mathrm{m}$ and cross sectional area $10^{-4}{\mathrm{m}}^2$ is heated from $0^{\circ }\mathrm{C}$ to $200^{\circ }\mathrm{C}$ without being allowed to extend or bend. The compressive tension produced in the rod is ____ $\times 10^4\mathrm{N}$. (Given Young's modulus of steel $=2\times 10^{11}\mathrm{N}{\mathrm{m}}^{-2}$, coefficient of linear expansion $=10^{-5}{\mathrm{K}}^{-1}$ )

    Show answer

    Answer: 4

20. Q522023 · 6 Apr 2023 · Shift 1· Numerical answer

    Two identical solid spheres each of mass $2\text{ kg}$ and radii $10\text{ cm}$ are fixed at the ends of a light rod. The separation between the centres of the spheres is $40\text{ cm}$. The moment of inertia of the system about an axis perpendicular to the rod passing through its middle point is ________ $\times 10^{-3}{\text{ kg m}}^2$

    Show answer

    Answer: 176

21. Q462023 · 6 Apr 2023 · Shift 2

    A child of mass $5\text{ kg}$ is going round a merry-go-round that makes $1$ rotation in $3.14\text{ s}$. The radius of the merry-go-round is $2\text{ m}$. The centrifugal force on the child will be

    1. A.$50\text{ N}$
    2. B.$80\text{ N}$
    3. C.$100\text{ N}$
    4. D.$40\text{ N}$
    Show answer

    Answer: D

22. Q592023 · 6 Apr 2023 · Shift 2· Numerical answer

    A ring and a solid sphere rotating about an axis passing through their centers have same radii of gyration. The axis of rotation is perpendicular to plane of ring. The ratio of radius of ring to that of sphere is $\sqrt{\frac{2}{x}}$. The value of $x$ is ___________.

    Show answer

    Answer: 5

23. Q532023 · 1 Feb 2023 · Shift 1· Numerical answer

    A light of energy $12.75\text{ eV}$ is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited state is $\frac{x}{\pi }\times 10^{-17}\text{ eVs}$. The value of $x$ is ________ (use $h=4.14\times 10^{-15}\text{ eVs},c=3\times 10^8{\text{ ms}}^{-1}$).

    Show answer

    Answer: 828

24. Q372023 · 31 Jan 2023 · Shift 1

    A rod with circular cross-section area $2{\text{ cm}}^2$ and length $40\text{ cm}$ is wound uniformly with 400 turns of an insulated wire. If a current of $0.4\text{ A}$ flows in the wire windings, the total magnetic flux produced inside windings is $4\pi \times 10^{-6}\text{ Wb}$. The relative permeability of the rod is (Given : Permeability of vacuum ${\mu }_0=4\pi \times 10^{-7}{\text{NA}}^{-2}$)

    1. A.$\frac{5}{16}$
    2. B.$125$
    3. C.$\frac{32}{5}$
    4. D.$12.5$
    Show answer

    Answer: B

25. Q572023 · 31 Jan 2023 · Shift 1· Numerical answer

    A thin rod having a length of $1\text{ m}$ and area of cross-section $3\times 10^{-6}{\text{ m}}^2$ is suspended vertically from one end. The rod is cooled from $210^{\circ }\text{C}$ to $160^{\circ }\text{C}$. After cooling, a mass $\mathrm{M}$ is attached at the lower end of the rod such that the length of rod again becomes $1\text{ m}$. Young's modulus and coefficient of linear expansion of the rod are $2\times 10^{11}{\text{ N m}}^{-2}$ and $2\times 10^{-5}{\text{ K}}^{-1}$, respectively. The value of $\mathrm{M}$ is ___________ kg. $\left(\text{Take }g=10{\text{ m s}}^{-2}\right)$

    Show answer

    Answer: 60