← Back to Physics-I

Rotational Motion

270 Questions Start Allen Test
All Exams Allen Advance Errorless
Q101 Allen 5. Angular Momentum & its Conservation MCQ
A child is standing on the edge of a merry-go-round that has the shape of a disk, as shown in the figure above. The mass of the child is 40 kilograms. The merry-go-round has a mass of 200 kilograms and a radius of 2.5 meters, and it is rotating with an angular velocity of $\omega = 2.0$ radians per second. The child then walks slowly toward the center of the merry-go-round. What will be the final angular velocity of the merry-go-round when the child reaches the center? (The size of the child can be neglected)
A.
2.0 rad/s
B.
2.2 rad/s
C.
2.4 rad/s
D.
2.8 rad/s
Q102 Allen 5. Angular Momentum & its Conservation MCQ
A uniform disk turns at 2.4 rev/s around a frictionless axis. A nonrotating rod, of the same mass as the disk and length equal to the disk's diameter is dropped onto the freely spinning disk figure. They then both turn around the axis with their centres superposed. What as the angular frequency in rev/s of the combination.
A.
1.2 rev/s
B.
2.0 rev/s
C.
1.44 rev/s
D.
0.96 rev/s
Q103 Allen 6. CRTM Kinematics MCQ
A disc is rolling without slipping with angular velocity $\omega$ . P and Q are two points equidistant from the centre C. The order of magnitude of velocity is :-
A.
$v_{Q} > v_{C} > v_{p}$
B.
$v_{P} > v_{C} > v_{Q}$
C.
$v_{P} = v_{C}, v_{Q} = v_{C} / 2$
D.
$v_{P} < v_{C} > v_{Q}$
Q104 Allen 6. CRTM Kinematics MCQ
In the following figure, a sphere of radius 3 m rolls on a plank. The accelerations of the sphere and the plank are indicated. The value of $\alpha$ is
A.
3 rad/s $^{2}$
B.
$6 \, rad/s^{2}$
C.
$3 \, rad/s^{2}$ (opposite to the direction shown in figure)
D.
$1\mathrm{rad} / s^{2}$
Q105 Allen 6. CRTM Kinematics MCQ
A disc of radius R is rolling purely on a flat horizontal surface, with a constant angular velocity. The angle between the velocity and acceleration vectors of point P is
A.
zero
B.
$45^{\circ}$
C.
$135^{\circ}$
D.
$\tan^{-1}(1/2)$
Q106 Allen 7. Dynamics MCQ
A cylinder is placed on a rough plank which in turn is placed on a smooth surface. The plank is pulled with a constant force F. The friction force can be given by which of the following diagrams
A.
B.
C.
D.
cannot be interpreted
Q107 Allen 8. Kinetic Energy MCQ
A body kept on a smooth horizontal surface is pulled by a constant horizontal force applied at the top point of the body. If the body rolls purely on the surface, its shape can be :
A.
thin pipe
B.
uniform cylinder
C.
uniform sphere
D.
thin spherical shell
Q108 Allen 8. Kinetic Energy MCQ
A hollow sphere of radius R and mass m is fully filled with non viscous liquid of mass m. It is rolled down a horizontal plane such that its centre of mass moves with a velocity v. If it purely rolls
A.
Kinetic energy of the sphere is $\frac{5}{6}mv^{2}$
B.
Kinetic energy of the sphere is $\frac{4}{5}mv^{2}$
C.
Angular momentum of the sphere about a fixed point on ground is $\frac{8}{3}mvR$
D.
Angular momentum of the sphere about a fixed point on ground is $\frac{14}{5}mvR$
Q109 Allen 8. Kinetic Energy MCQ
A sphere of mass M and radius R is attached by a light rod of length $\ell$ to a point P. The sphere rolls without slipping on a circular track as shown. It is released from the horizontal position. The angular momentum of the system about P when the rod becomes vertical is :
A.
$M\sqrt{\frac{10}{7}gl}[l + R]$
B.
$M\sqrt{\frac{10}{7}gl}\left[l + \frac{2}{5}R\right]$
C.
$M \sqrt{\frac{10}{7} gl} \left[ l + \frac{7}{5} R \right]$
D.
$M\sqrt{\frac{10}{7}gl}\left[l - \frac{2}{5}R\right]$
Q110 Allen 8. Kinetic Energy MCQ
A thin table cloth covers a horizontal table and a uniform body of round shape lies on top of it. The table cloth is pulled from under the body, and friction causes the body to slide and rotate. What is the body's final motion on the table? (Assume that the table is so large that the body does not fall off it.)
A.
Body will finally roll towards left
B.
Body will finally roll towards right
C.
Body will finally come to rest
D.
Any of the above is possible depending on shape of body
Q111 Allen 8. Kinetic Energy MCQ
A ball rolls down an inclined plane as shown in figure. The ball is first released from rest from P and then later from Q. Which of the following statement is/are correct? (i) The ball takes twice as much time to roll from Q to O as it does to roll from P to O. (ii) The acceleration of the ball at Q is twice as large as the acceleration at P. (iii) The ball has twice as much K.E. at O when rolling from Q as it does when rolling from P.
A.
i, ii only
B.
ii, iii only
C.
i only
D.
iii only
Q112 Allen 8. Kinetic Energy MCQ
A metal ball of mass m is put at the point A of a loop tract and the vertical distance of A from the lower most point of tract is n times the radius R of the circular part. The linear velocity of ball when it rolls to the point B to a height R in the circular tract will be
A.
$\sqrt{\frac{5g(n - 1)R}{7}}$
B.
$\sqrt{\frac{10g(n - 1)R}{7}}$
C.
$\sqrt{\frac{5g(n+1)R}{7}}$
D.
$\sqrt{\frac{10g(n+1)R}{7}}$
Q113 Allen 9. Angular Momentum in CRTM MCQ
A ring of mass m is thrown in horizontal direction on a rough horizontal surface with a speed $v_{0}$ . The speed of the ring, when it starts pure rolling, is ā€“
A.
$\frac{v_{0}}{2}$
B.
$\frac{v_{0}}{3}$
C.
$\frac{2v_{0}}{3}$
D.
$\frac{3v_{0}}{3}$
Q114 Allen 9. Angular Momentum in CRTM MCQ
A solid sphere of mass M and radius r slips on a rough horizontal plane. At some instant it has translational velocity $v_{0}$ and rotational velocity about the centre $v_{0}/2r$ . The translational velocity after the sphere starts pure rolling
A.
$6v_{0}/7$ in forward direction
B.
$6v_{0}/7$ in backward direction
C.
$7v_{0}/6$ in forward direction
D.
$6v_{0}/6$ in backward direction
Q115 Allen 9. Angular Momentum in CRTM MCQ
A hollow sphere is moving with linear velocity and angular velocity as shown in figure. The time after which pure rolling starts is :
A.
$\frac{2v}{3\mu g}$
B.
$\frac{4v}{7\mu g}$
C.
$\frac{4v}{5\mu g}$
D.
$\frac{5v}{4\mu g}$
Q116 Allen 9. Angular Momentum in CRTM MCQ
A uniform circular disc placed on a rough horizontal surface has initially a velocity $v_{0}$ and an angular velocity $\omega_{0}$ as shown in the figure. The disc comes to rest after moving some distance in the direction of motion. Then $\frac{v_{0}}{r\omega_{0}}$ is
A.
$\frac {1}{2}$
B.
1
C.
$\frac {3}{2}$
D.
2
Q117 Allen 10. Rolling MCQ
A solid sphere is under pure rolling on a rough fixed incline plane of angle $\theta$ . Choose the correct options if only contact forces and gravity are acting :
A.
Frictional force will be down the incline if sphere rolls up the incline and it will be up the incline if sphere rolls down the incline.
B.
Frictional force will be down the incline whether spheres rolls up the incline or down the incline
C.
Frictional force and acceleration of the body will increase with the increase in angle of incline plane
D.
Velocity and acceleration of the point of contact of sphere with incline will be zero during the motion.
Q118 Allen 10. Rolling MCQ
A solid uniform disk of mass m rolls without slipping down a fixed inclined plane with an acceleration a. The frictional force on the disk due to surface of the plane is:
A.
2 ma
B.
3/2 ma
C.
ma
D.
1/2 ma
Q119 Allen 10. Rolling MCQ
The cylinder shown, with mass M and radius R, has a radially dependent density. The cylinder starts from rest and rolls without slipping down an inclined plane of height H. At the bottom of the plane its translational speed is $(8gH/7)^{1/2}$ . Which of the following is the rotational inertia of the cylinder?
A.
$\frac {1}{2} M R ^ {2}$
B.
$\frac{3}{4} MR^2$
C.
$\frac{7}{8} MR^2$
D.
$\mathrm{MR}^2$
Q120 Allen 10. Rolling MCQ
A uniform disk of mass m and radius R rolls without slipping down an incline plane of length l and inclination $\theta$ . Initially the disk was at rest at the top of the incline plane. Its angular momentum about the point of contact with the inclined plane when it reaches the bottom will be equal to:
A.
$\sqrt{4m^{2}R^{2}gl\sin\theta}$
B.
$\sqrt{3m^{2}R^{2}gl\sin\theta}$
C.
$\sqrt{\frac{m^{2}R^{2}gl\sin\theta}{4}}$
D.
zero
Q121 Allen 10. Rolling MCQ
A cylinder rolls up an inclined plane, reaches some height, and then rolls down (without slipping throughout these motions). The directions of the frictional force acting on the cylinder are
A.
Up the incline while ascending and down the incline while descending
B.
Up the incline while ascending as well as descending
C.
down the incline while ascending and up the incline while descending
D.
down the incline while ascending as well as descending
Q122 Allen 10. Rolling MCQ
A plank of mass M is placed over smooth inclined plane and a sphere is also placed over the plank. Friction is sufficient between sphere and plank. If plank and sphere are released from rest, the frictional force on sphere is:
A.
up the plane
B.
down the plane
C.
horizontal
D.
zero
Q123 Allen 11. Impulse & Angular Impulse MCQ
A force F is applied to a dumbbell for a time interval, t, first as in (i) and then as in (ii). In which case does the dumbbell acquire the greater centre-of-mass speed?
A.
(i)
B.
(ii)
C.
there is no difference
D.
the answer depends on the rotational inertia of the dumbbell
Q124 Allen 11. Impulse & Angular Impulse MCQ
A uniform rod of length l and mass M rotating about a fixed vertical axis on a smooth horizontal table. It elastically strikes a particle placed at a distance l/3 from its axis and stops. Mass of the particle is
A.
$3M$
B.
$\frac{3M}{4}$
C.
$\frac{3M}{2}$
D.
$\frac{4M}{3}$
Q125 Allen 11. Impulse & Angular Impulse MCQ
A mass m is moving at speed v perpendicular to a rod of length d and mass M = 6m which pivots around a frictionless axle running through its centre. It strikes and sticks to the end of the rod. The moment of inertia of the rod about its centre is $Md^{2}/12$ . Then the angular speed of the system right after the collision is
A.
2v/d
B.
2v/(3d)
C.
v/d
D.
3v/(2d)