2011
NEET
MCQ
AIPMT 2011 Prelims
The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is $I$0. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is
A.
${I_0} + M{L^2}/2$
B.
${I_0} + M{L^2}/4$
C.
${I_0} + 2M{L^2}$
D.
${I_0} + M{L^2}$
2011
NEET
MCQ
AIPMT 2011 Prelims
The instantaneous angular position of a point on a rotating wheel is given by the equation $\theta \left( t \right) = 2{t^3} - 6{t^2}$
The torque on the wheel becomes zero at
The torque on the wheel becomes zero at
A.
t = 1 s
B.
t = 0.5 s
C.
t = 0.25 s
D.
t = 2 s
2010
NEET
MCQ
AIPMT 2010 Mains
A solid cylinder and a hollow cylinder, both of the same mass and same external diameter are released from the same height at the same time on an inclined plane. Both roll down without slipping. Which one will reach the bottom first?
A.
Both together only when angle of inclination of plane is 45o
B.
Both together
C.
Hollow cylinder
D.
Solid cylinder
2010
NEET
MCQ
AIPMT 2010 Mains
From a circular disc of radius R and mass 9M, a small disc of mass M and radius ${R \over 3}$ is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre is
A.
${{40} \over 9}$ MR2
B.
MR2
C.
4MR2
D.
${4 \over 9}$ MR2
2010
NEET
MCQ
AIPMT 2010 Mains
A thin circular ring of mass M and radius r is rotating about its axis with constant angular velocity $\omega $. Two objects each of msass m are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with angular velocity given by
A.
${{\left( {M + 2m} \right)\omega } \over {2m}}$
B.
${{2M\omega } \over {M + 2m}}$
C.
${{\left( {M + 2m} \right)\omega } \over M}$
D.
${{M\omega } \over {M + 2m}}$
2010
NEET
MCQ
AIPMT 2010 Prelims
A circular disk of moment of inertia ${I_t}$ is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed ${\omega _i}$. Another disk of moment of inertia ${I_b}$ is dropped coaxially onto the rotating disk. Initially the second disk has zero angular speed. Eventually both the disks rotate with a constant angular speed $\omega $. The energy lost by the initially rotating disc to friction is
A.
${1 \over 2}{{I_b^2} \over {\left( {{I_t} + {I_b}} \right)}}\omega _i^2$
B.
${1 \over 2}{{I_t^2} \over {\left( {{I_t} + {I_b}} \right)}}\omega _i^2$
C.
${{{I_b} - {I_t}} \over {\left( {{I_t} + {I_b}} \right)}}\omega _i^2$
D.
${1 \over 2}{{{I_b}{I_t}} \over {\left( {{I_t} + {I_b}} \right)}}\omega _i^2$
2010
NEET
MCQ
AIPMT 2010 Prelims
A gramophone record is revolving with an angular velocity $\omega $. A coin is placed at a distance r from the centre of the record. The static coefficient of friction is $\mu $. The coin will revolve with the record if
A.
r = $\mu $g$\omega $2
B.
r < ${{{\omega ^2}} \over {\mu g}}$
C.
$r \le {{\mu g} \over {{\omega ^2}}}$
D.
$r \ge {{\mu g} \over {{\omega ^2}}}$
2009
NEET
MCQ
AIPMT 2009
Four identical thin rods each of mass M and length $l$, form a square frame. Moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is
A.
${2 \over 3}M{l^2}$
B.
${{13} \over 3}M{l^2}$
C.
${1 \over 3}M{l^2}$
D.
${4 \over 3}M{l^2}$
2009
NEET
MCQ
AIPMT 2009
If $\overrightarrow F $ is the force acting on a particle having position vector $\overrightarrow r $ and $\overrightarrow \tau $ be the torque of this force about the origin, then
A.
$\overrightarrow r .\overrightarrow \tau > 0$ and $\overrightarrow F .\overrightarrow \tau < 0$
B.
$\overrightarrow r .\overrightarrow \tau = 0$ and $\overrightarrow F .\overrightarrow \tau = 0$
C.
$\overrightarrow r .\overrightarrow \tau = 0$ and $\overrightarrow F .\overrightarrow \tau \ne 0$
D.
$\vec r.\vec \tau \ne 0$ and $\overrightarrow F .\overrightarrow \tau = 0$
2009
NEET
MCQ
AIPMT 2009
A thin circular ring of mass M and radius R is rotating in a horizontal plane about an axis vertical to its plane with a constant angular velocity $\omega $. If two objects each of mass m be attached gently to the opposite ends of a diameter of the ring, the ring will then rotate with an angular velocity
A.
${{\omega M} \over {M + 2m}}$
B.
${{\omega \left( {M + 2m} \right)} \over M}$
C.
${{\omega M} \over {M + m}}$
D.
${{\omega \left( {M - 2m} \right)} \over {M + 2m}}$
2008
NEET
MCQ
AIPMT 2008
The ratio of the radii of gyration of a circular disc to that of a circular ring, each of same mass and radius, around their respective axes is
A.
$\sqrt 2 :1$
B.
$\sqrt 2 :\sqrt 3 $
C.
$\sqrt 3 :\sqrt 2 $
D.
$1:\sqrt 2 $
2008
NEET
MCQ
AIPMT 2008
A thin rod of length L and mass M is bent at its midpoint into two halves so that the angle between them is 90o. The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is
A.
${{M{L^2}} \over 6}$
B.
${{\sqrt 2 M{L^2}} \over {24}}$
C.
${{M{L^2}} \over {24}}$
D.
${{M{L^2}} \over {12}}$
2007
NEET
MCQ
AIPMT 2007
A particle of mass m moves in the XY plane with a velocity v along the straight line AB. If the angular momentum of the particle with respect to origin O is LA when it is at A and LB when it is at B, then
A.
LA = LB
B.
the relationship between LA and LB depends upon the slope of the line AB
C.
LA < LB
D.
LA > LB.
2007
NEET
MCQ
AIPMT 2007
A wheel has angular acceleration of 3.0 rad/sec2 and an initial angular speed of 2.00 rad/sec. In a time of 2 sec it has rotated through an angle (in radian) of
A.
10
B.
12
C.
4
D.
6
2007
NEET
MCQ
AIPMT 2007
A uniform rod AB of length $l$ and mass m is free to rotate about point A. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about A is ml2/3, the initial angular acceleration of the rod will be
A.
${{mgl} \over 2}$
B.
${3 \over 2}gl$
C.
${{3g} \over {2l}}$
D.
${{2g} \over {3l}}$
2006
NEET
MCQ
AIPMT 2006
The moment of inertia of a uniform circular disc of radius R and mass M about an axis touching the disc at its diameter and normal to the disc
A.
${1 \over 2}$MR2
B.
MR2
C.
${2 \over 5}M{R^2}$
D.
${3 \over 2}M{R^2}$
2006
NEET
MCQ
AIPMT 2006
A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity $\omega $. The force exerted by the liquid at the other end is
A.
${{M{L^2}{\omega ^2}} \over 2}$
B.
${{ML{\omega ^2}} \over 2}$
C.
${{M{L^2}\omega } \over 2}$
D.
$ML{\omega ^2}$
2006
NEET
MCQ
AIPMT 2006
A uniform rod AB of length $l$ and mass m is free to rotate about point A. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about A is ml2/3, the initial angular acceleration of the rod will be
A.
${{mgl} \over 2}$
B.
${3 \over 2}gl$
C.
${{3g} \over {2l}}$
D.
${{2g} \over {3l}}$
2005
NEET
MCQ
AIPMT 2005
A drum of radius R and mass M, rolls down without slipping along an inclined plane of angle $\theta $. The frictional force
A.
dissipates energy as heat
B.
decreases the rotational motion
C.
decreases the rotational and translation motion
D.
converts translational energy to rotational energy.
2005
NEET
MCQ
AIPMT 2005
The moment of inertia of a uniform circular disc of radius R and mass M about an axis passing from the edge of the disc and normal to the disc is
A.
MR2
B.
${1 \over 2}$ MR2
C.
${3 \over 2}$ MR2
D.
${7 \over 2}$ MR2
2005
NEET
MCQ
AIPMT 2005
Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular velocity will be in the ratio
A.
2 : 1
B.
1 : 2
C.
$\sqrt 2 :1$
D.
$1:\sqrt 2 $
2004
NEET
MCQ
AIPMT 2004
The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axes in the plane of the ring is
A.
2 : 3
B.
2 : 1
C.
$\sqrt 5 :\sqrt 6 $
D.
$1:\sqrt 2 $
2004
NEET
MCQ
AIPMT 2004
A wheel having moment of inertia 2 kg m2 about its vertical axis, rotates at the rate of 60 rpm about this axis. The torque which can stop the wheel's rotation in one minute would be
A.
${{2\pi } \over {15}}$ N m
B.
${\pi \over {12}}$ N m
C.
${\pi \over {15}}$ N m
D.
${\pi \over {18}}$ N m
2004
NEET
MCQ
AIPMT 2004
Three particles, each of mass m gram, are situated at the vertices of an equilateral triangle ABC of side $l$ cm (as shown in the figure). The moment of inertia of the system about a line AX perpendicular to AB and in the plane of ABC, in gram-cm2 units will be
A.
${3 \over 4}$m$l$2
B.
2m$l$2
C.
${5 \over 4}$m$l$2
D.
${3 \over 2}$m$l$2
2004
NEET
MCQ
AIPMT 2004
A round disc of moment of inertia $I$2 about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia $I$1 rotating with an angular velocity $\omega $ about the same axis. The final angular velocity of the combination of discs is
A.
${{{I_2}\omega } \over {{I_1} + {I_2}}}$
B.
$\omega $
C.
${{{I_1}\omega } \over {{I_1} + I{}_2}}$
D.
${{\left( {{I_1} + {I_2}} \right)\omega } \over {{I_1}}}$
2003
NEET
MCQ
AIPMT 2003
A solid cylinder of mass M and radius R rolls without slipping down an inclined plane of length L and height h. What is the speed of its centre of mass when the cylinder reaches its bottom ?
A.
$\sqrt {2gh} $
B.
$\sqrt {{3 \over 4}gh} $
C.
$\sqrt {{4 \over 3}gh} $
D.
$\sqrt {4gh} $
2003
NEET
MCQ
AIPMT 2003
A stone is tied to a string of length $l$ and is whirled in a vertical circle with the other end of the string as the centre. At a certain instant of time, the stone is at its lowest position and has a speed u. The magnitude of the change in velocity as it reaches a position where the string is horizontal (g being acceleration due to gravity) is
A.
$\sqrt {2\left( {{\mu ^2} - gl} \right)} $
B.
$\sqrt {{u^2} - gl} $
C.
$u - \sqrt {{u^2} - 2gl} $
D.
$\sqrt {2gl} $
2003
NEET
MCQ
AIPMT 2003
A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity $\omega $. Four objects each of mass m, are kept gently to the opposite ends of two perpendicular diameters of the ring. The angular velocity of the ring will be :
A.
${{M\omega } \over {4m}}$
B.
${{M\omega } \over {M + 4m}}$
C.
${{\left( {M + 4m} \right)\omega } \over M}$
D.
${{\left( {M - 4m} \right)\omega } \over {M + 4m}}$
2003
NEET
MCQ
AIPMT 2003
A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is K. If radius of the ball be R. then the fraction of total energy associated with its rotational energy will be
A.
${{{K^2} + {R^2}} \over {{R^2}}}$
B.
${{{K^2}} \over {{R^2}}}$
C.
${{{K^2}} \over {{K^2} + {R^2}}}$
D.
${{{R^2}} \over {{K^2} + {R^2}}}$
2002
NEET
MCQ
AIPMT 2002
A disc is rotating with angular speed $\omega $. If a child sits on it, what is conserved
A.
linear momentum
B.
angular momentum
C.
kinetic energy
D.
potential energy.
2002
NEET
MCQ
AIPMT 2002
A solid sphere of radius R is placed on smooth horizontal surface. A horizontal force F is applied at height h from the lowest point. For the maximum acceleration of centre of mass, which is correct ?
A.
h = R
B.
h = 2R
C.
h = 0
D.
no relation between h and R.
2002
NEET
MCQ
AIPMT 2002
A point P consider at contact point of a wheel on ground which rolls on ground without slipping then value of displacement of point P when wheel completes half of rotation (if radius of wheel is 1 m)
A.
2 m
B.
$\sqrt {{\pi ^2} + 4} m$
C.
$\pi \,m$
D.
$\sqrt {{\pi ^2} + 2} \,m$
2002
NEET
MCQ
AIPMT 2002
A circular disc is to be made by using iron and aluminium so that it acquired maximum moment of inertia about geometrical axis. It is possible with
A.
aluminium at interior and iron surround to it
B.
iron at interior and aluminium surround to it
C.
using iron and aluminium layers in alternate order
D.
sheet of iron is used at both external surface and aluminium sheet as internal layers.
2000
NEET
MCQ
AIPMT 2000
For a hollow cylinder and a solid cylinder rolling without slipping on an inclined plane, then which of these reaches earlier
A.
solid cylinder
B.
hollow cylinder
C.
both simultaneously
D.
can't say anything.
2000
NEET
MCQ
AIPMT 2000
For the adjoining diagram, the correct relation between I1, I2, and I3 is, (I-moment of inertia)
A.
I1 > I2
B.
I2 > I1
C.
I3 > I1
D.
I3 > I2
2000
NEET
MCQ
AIPMT 2000
As shown in the figure at point O a mass is performing vertical circular motion. The average velocity of the particle is increased, then at which point will the string break
A.
A
B.
B
C.
C
D.
D