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

2023 41 questions

1. 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 _________.

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   Answer: 3

2. 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 ___________.

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   Answer: 1

3. 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.$x(t)=r\sin \left(\omega t+\frac{\pi }{6}\right)$
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   Answer: C

4. 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
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   Answer: D

5. 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
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   Answer: B

6. 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 $=10^{-5}{\mathrm{K}}^{-1}$ )

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   Answer: 4

7. 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 ________ $\times 10^{-3}{\text{ kg m}}^2$

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   Answer: 176

8. 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.$40\text{ N}$
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   Answer: D

9. 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 ___________.

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   Answer: 5

10. 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 $h=4.14\times 10^{-15}\text{ eVs},c=3\times 10^8{\text{ ms}}^{-1}$).

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    Answer: 828

11. 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.$12.5$
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    Answer: B

12. 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. $\left(\text{Take }g=10{\text{ m s}}^{-2}\right)$

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    Answer: 60

13. Q312023 · 31 Jan 2023 · Shift 2

    For a solid rod, the Young's modulus of elasticity is $3.2\times 10^{11}{\text{Nm}}^{-2}$ and density is $8\times 10^3{\text{ kg m}}^{-3}$. The velocity of longitudinal wave in the rod will be.

    1. A.$3.65\times 10^3{\text{ ms}}^{-1}$
    2. B.$6.32\times 10^3{\text{ ms}}^{-1}$
    3. C.$18.96\times 10^3{\text{ ms}}^{-1}$
    4. D.$145.75\times 10^3{\text{ ms}}^{-1}$
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    Answer: B

14. Q322023 · 31 Jan 2023 · Shift 2

    Heat energy of $735\text{ J}$ is given to a diatomic gas allowing the gas to expand at constant pressure. Each gas molecule rotates around an internal axis but do not oscillate. The increase in the internal energy of the gas will be :

    1. A.$572\text{ J}$
    2. B.$441\text{ J}$
    3. C.$525\text{ J}$
    4. D.$735\text{ J}$
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    Answer: C

15. Q442023 · 31 Jan 2023 · Shift 2

    Match List I with List II | LIST I | LIST II | | :--- | :--- | | A. Angular momentum | I. $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]$ | | B. Torque | II. $\left[{\mathrm{ML}}^{-2}{\mathrm{T}}^{-2}\right]$ | | C. Stress | III. $\left[{\mathrm{ML}}^2{\mathrm{T}}^{-1}\right]$ | | D. Pressure gradient | IV. $\left[{\mathrm{ML}}^{-1}{\mathrm{T}}^{-2}\right]$ | Choose the correct answer from the options given below:

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

16. Q572023 · 31 Jan 2023 · Shift 2· Numerical answer

    Two discs of same mass and different radii are made of different materials such that their thicknesses are $1\text{ cm}$ and $0.5\text{ cm}$ respectively. The densities of materials are in the ratio $3:5$. The moment of inertia of these discs respectively about their diameters will be in the ratio of $\frac{x}{6}$. The value of $x$ is ___________.

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    Answer: 5

17. Q552023 · 30 Jan 2023 · Shift 1· Numerical answer

    A thin uniform rod of length $2\text{ m}$, cross sectional area '$A$' and density '$d$' is rotated about an axis passing through the centre and perpendicular to its length with angular velocity $\omega$. If value of $\omega$ in terms of its rotational kinetic energy $E$ is $\sqrt{\frac{\alpha E}{Ad}}$ then value of $\alpha$ is ___________.

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    Answer: 3

18. Q522023 · 29 Jan 2023 · Shift 1· Numerical answer

    A solid sphere of mass 2 kg is making pure rolling on a horizontal surface with kinetic energy 2240 J. The velocity of centre of mass of the sphere will be ____ $\mathrm{m}{\mathrm{s}}^{-1}$.

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    Answer: 40

19. Q552023 · 29 Jan 2023 · Shift 1· Numerical answer

    As shown in the figure, three identical polaroids ${\mathrm{P}}_1$, ${\mathrm{P}}_2$ and ${\mathrm{P}}_3$ are placed one after another. The pass axis of ${\mathrm{P}}_2$ and ${\mathrm{P}}_3$ are inclined at angle of $60^{\circ }$ and $90^{\circ }$ with respect to axis of ${\mathrm{P}}_1$. The source S has an intensity of 256 $\frac{W}{m^2}$. The intensity of light at point O is ____ $\frac{W}{m^2}$.

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    Answer: 24

20. Q512023 · 29 Jan 2023 · Shift 2· Numerical answer

    A particle of mass 100 g is projected at time t = 0 with a speed 20 $\mathrm{m}{\mathrm{s}}^{-1}$ at an angle $45^{\circ }$ to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time t = 2s is found to be $\sqrt{\mathrm{K}}\mathrm{kg}{\mathrm{m}}^2/s$. The value of K is ____. (Take $g=10\mathrm{m}{\mathrm{s}}^{-2}$)

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    Answer: 800

21. Q442023 · 25 Jan 2023 · Shift 1
    
    1. A.90 N
    2. B.240 N
    3. C.30 N
    4. D.300 N
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    Answer: D

22. Q522023 · 25 Jan 2023 · Shift 1· Numerical answer

    ${\mathrm{I}}_{\mathrm{CM}}$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc. ${\mathrm{I}}_{\mathrm{AB}}$ is its moment of inertia about an axis AB perpendicular to plane and parallel to axis CM at a distance $\frac{2}{3}$R from center. Where R is the radius of the disc. The ratio of ${\mathrm{I}}_{\mathrm{AB}}$ and ${\mathrm{I}}_{\mathrm{CM}}$ is $x:9$. The value of $x$ is ____.

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    Answer: 17

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

    As shown in the figure, in an experiment to determine Young's modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of $45^{\circ }$ with the load axis. The length of wire is 62.8 cm and its diameter is 4 mm. The Young's modulus is found to be $x\times 10^4\mathrm{N}{\mathrm{m}}^{-2}$. The value of $x$ is ____.

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    Answer: 5

24. Q562023 · 25 Jan 2023 · Shift 2· Numerical answer

    If a solid sphere of mass 5 kg and a disc of mass 4 kg have the same radius. Then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be $\frac{x}{7}$. The value of $x$ is ____.

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    Answer: 5

25. Q552023 · 24 Jan 2023 · Shift 1· Numerical answer
    
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    Answer: 110