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

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.

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

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 ____.

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 ____.

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.$\frac{\sqrt{3}}{16}\frac{{\mathrm{mu}}^3}{\mathrm{g}}$

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)

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 $\text{g}=10{\text{ m/s}}^2$).

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 _________ $\mathrm{kg}{\mathrm{m}}^2{\mathrm{s}}^{-1}$.

A heavy iron bar of weight $12\text{ kg}$ is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle $60^{\circ }$ with the horizontal, the normal force applied by the man on bar is :

1. A.$3\text{ kg-wt}$
2. B.$6\text{ kg-wt}$
3. C.$6\sqrt{3}\text{ kg-wt}$
4. D.$12\text{ kg-wt}$

When a polaroid sheet is rotated between two crossed polaroids then the transmitted light intensity will be maximum for a rotation of :

1. A.$90^{\circ }$
2. B.$30^{\circ }$
3. C.$45^{\circ }$
4. D.$60^{\circ }$

1. A.$27\text{ Pa}$
2. B.$175\text{ Pa}$
3. C.$135\text{ Pa}$
4. D.$36\text{ Pa}$

1. A.$R\sqrt{({\pi }^2+1)}$
2. B.$2R$
3. C.$R\sqrt{({\pi }^2+4)}$
4. D.$2R\sqrt{(1+4{\pi }^2)}$

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 ___________ $\text{rad/s}$.

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 ___________ ${\text{rad s}}^{-2}$.

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

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

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

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 _________.

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 _________.

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 _________.

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

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

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