System of Particles & Rotational Motion Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. The moment of inertia of a body about a given axis is 1.2 kg m
2
.
Initially, the body is at rest. In order to produce a rotational kinetic
energy of 1500 joule, an angular acceleration of 25  radian/sec
2
 must be
applied about that axis for a duration of
(a) 4 seconds
(b) 2 seconds
(c) 8 seconds
(d) 10 seconds
2. A pulley of radius 2 m is rotated about its axis by a force F = (20t – 5t
2
)
newton (where t is measured in seconds) applied tangentially. If the
moment of inertia of the pulley about its axis of rotation is 10 kg-m
2
 the
number of rotations made by the pulley before its direction of motion is
reversed, is:
(a) more than 3 but less than 6
(b) more than 6 but less than 9
(c) more than 9
(d) less than 3
Page 2


PART-I (Single Correct MCQs)
1. The moment of inertia of a body about a given axis is 1.2 kg m
2
.
Initially, the body is at rest. In order to produce a rotational kinetic
energy of 1500 joule, an angular acceleration of 25  radian/sec
2
 must be
applied about that axis for a duration of
(a) 4 seconds
(b) 2 seconds
(c) 8 seconds
(d) 10 seconds
2. A pulley of radius 2 m is rotated about its axis by a force F = (20t – 5t
2
)
newton (where t is measured in seconds) applied tangentially. If the
moment of inertia of the pulley about its axis of rotation is 10 kg-m
2
 the
number of rotations made by the pulley before its direction of motion is
reversed, is:
(a) more than 3 but less than 6
(b) more than 6 but less than 9
(c) more than 9
(d) less than 3
3. A gymnast takes turns with her arms and legs stretched. When she pulls
her arms and legs in
(a) the angular velocity decreases
(b) the moment of inertia decreases
(c) the angular velocity stays constant
(d) the angular momentum increases
4. An equilateral triangle ABC formed from a uniform
wire has two small identical beads initially located at
A. The triangle is set rotating about the vertical axis AO. Then the beads
are released from rest simultaneously and
allowed to slide down, one along AB and the other along AC as shown.
Neglecting frictional effects, the quantities that are conserved as the
beads slide down, are
(a) angular velocity and total energy (kinetic and potential)
(b) total angular momentum and total energy
(c) angular velocity and moment of inertia about the axis of rotation
(d) total angular momentum and moment of inertia about the axis of rotation
5. Two identical discs of mass m and radius r are arranged as shown in the
figure. If a is the angular acceleration of the lower disc and a
cm
 is
acceleration of centre of mass of the lower disc, then relation between
a
cm
,
a and r is
(a) a
cm
 = a/r
(b) a
cm
 = 2ar
(c) a
cm
 = a r
(d) None of these
6. A tennis ball (treated as hollow spherical shell) starting
from O rolls down a hill. At point A the ball becomes air borne leaving
at an angle of 30° with the horizontal. The ball strikes the ground at B.
What is the value of the distance AB ?
(Moment of inertia of a spherical shell of mass m and radius R about its
diameter 
(a) 1.87 m
Page 3


PART-I (Single Correct MCQs)
1. The moment of inertia of a body about a given axis is 1.2 kg m
2
.
Initially, the body is at rest. In order to produce a rotational kinetic
energy of 1500 joule, an angular acceleration of 25  radian/sec
2
 must be
applied about that axis for a duration of
(a) 4 seconds
(b) 2 seconds
(c) 8 seconds
(d) 10 seconds
2. A pulley of radius 2 m is rotated about its axis by a force F = (20t – 5t
2
)
newton (where t is measured in seconds) applied tangentially. If the
moment of inertia of the pulley about its axis of rotation is 10 kg-m
2
 the
number of rotations made by the pulley before its direction of motion is
reversed, is:
(a) more than 3 but less than 6
(b) more than 6 but less than 9
(c) more than 9
(d) less than 3
3. A gymnast takes turns with her arms and legs stretched. When she pulls
her arms and legs in
(a) the angular velocity decreases
(b) the moment of inertia decreases
(c) the angular velocity stays constant
(d) the angular momentum increases
4. An equilateral triangle ABC formed from a uniform
wire has two small identical beads initially located at
A. The triangle is set rotating about the vertical axis AO. Then the beads
are released from rest simultaneously and
allowed to slide down, one along AB and the other along AC as shown.
Neglecting frictional effects, the quantities that are conserved as the
beads slide down, are
(a) angular velocity and total energy (kinetic and potential)
(b) total angular momentum and total energy
(c) angular velocity and moment of inertia about the axis of rotation
(d) total angular momentum and moment of inertia about the axis of rotation
5. Two identical discs of mass m and radius r are arranged as shown in the
figure. If a is the angular acceleration of the lower disc and a
cm
 is
acceleration of centre of mass of the lower disc, then relation between
a
cm
,
a and r is
(a) a
cm
 = a/r
(b) a
cm
 = 2ar
(c) a
cm
 = a r
(d) None of these
6. A tennis ball (treated as hollow spherical shell) starting
from O rolls down a hill. At point A the ball becomes air borne leaving
at an angle of 30° with the horizontal. The ball strikes the ground at B.
What is the value of the distance AB ?
(Moment of inertia of a spherical shell of mass m and radius R about its
diameter 
(a) 1.87 m
(b) 2.08 m
(c) 1.57 m
(d) 1.77 m
7. A hollow sphere is held suspended. Sand is now
poured into it in stages.
The centre of mass of the sphere with
the sand
(a) rises continuously
(b) remains unchanged in the process
(c) first rises and then falls to the
original position
(d) first falls and then rises to the original position
8. From a solid sphere of mass M and radius R a cube of maximum
possible volume is cut. Moment of inertia of cube about an axis passing
through its center and perpendicular to one of its faces is :
(a)
(b)
(c)
(d)
9. A solid sphere is rolling on a surface as shown in figure, with a
translational velocity v m s
–1
. If it is to climb the inclined surface
continuing to roll without slipping, then minimum velocity for this to
happen is
(a)
(b)
Page 4


PART-I (Single Correct MCQs)
1. The moment of inertia of a body about a given axis is 1.2 kg m
2
.
Initially, the body is at rest. In order to produce a rotational kinetic
energy of 1500 joule, an angular acceleration of 25  radian/sec
2
 must be
applied about that axis for a duration of
(a) 4 seconds
(b) 2 seconds
(c) 8 seconds
(d) 10 seconds
2. A pulley of radius 2 m is rotated about its axis by a force F = (20t – 5t
2
)
newton (where t is measured in seconds) applied tangentially. If the
moment of inertia of the pulley about its axis of rotation is 10 kg-m
2
 the
number of rotations made by the pulley before its direction of motion is
reversed, is:
(a) more than 3 but less than 6
(b) more than 6 but less than 9
(c) more than 9
(d) less than 3
3. A gymnast takes turns with her arms and legs stretched. When she pulls
her arms and legs in
(a) the angular velocity decreases
(b) the moment of inertia decreases
(c) the angular velocity stays constant
(d) the angular momentum increases
4. An equilateral triangle ABC formed from a uniform
wire has two small identical beads initially located at
A. The triangle is set rotating about the vertical axis AO. Then the beads
are released from rest simultaneously and
allowed to slide down, one along AB and the other along AC as shown.
Neglecting frictional effects, the quantities that are conserved as the
beads slide down, are
(a) angular velocity and total energy (kinetic and potential)
(b) total angular momentum and total energy
(c) angular velocity and moment of inertia about the axis of rotation
(d) total angular momentum and moment of inertia about the axis of rotation
5. Two identical discs of mass m and radius r are arranged as shown in the
figure. If a is the angular acceleration of the lower disc and a
cm
 is
acceleration of centre of mass of the lower disc, then relation between
a
cm
,
a and r is
(a) a
cm
 = a/r
(b) a
cm
 = 2ar
(c) a
cm
 = a r
(d) None of these
6. A tennis ball (treated as hollow spherical shell) starting
from O rolls down a hill. At point A the ball becomes air borne leaving
at an angle of 30° with the horizontal. The ball strikes the ground at B.
What is the value of the distance AB ?
(Moment of inertia of a spherical shell of mass m and radius R about its
diameter 
(a) 1.87 m
(b) 2.08 m
(c) 1.57 m
(d) 1.77 m
7. A hollow sphere is held suspended. Sand is now
poured into it in stages.
The centre of mass of the sphere with
the sand
(a) rises continuously
(b) remains unchanged in the process
(c) first rises and then falls to the
original position
(d) first falls and then rises to the original position
8. From a solid sphere of mass M and radius R a cube of maximum
possible volume is cut. Moment of inertia of cube about an axis passing
through its center and perpendicular to one of its faces is :
(a)
(b)
(c)
(d)
9. A solid sphere is rolling on a surface as shown in figure, with a
translational velocity v m s
–1
. If it is to climb the inclined surface
continuing to roll without slipping, then minimum velocity for this to
happen is
(a)
(b)
(c)
(d)
10. A loop of radius r and mass m rotating with an
angular velocity ?
0
 is placed on a rough
horizontal surface. The initial velocity of the centre of the hoop is
zero.What will be the velocity of the centre of the hoop when it ceases
to slip?
(a)
(b)
(c)
(d) r?
0
11. A thin rod of length ‘L’ is lying along the x-axis with its ends at x = 0
and x = L. Its linear density 
(mass/length) varies with x as ,
where n can be zero or any positive number. If the position x
CM
 of the
centre of mass of the rod is plotted against ‘n’, which of the following
graphs best approximates the dependence of x
CM
 on n?
(a)
Page 5


PART-I (Single Correct MCQs)
1. The moment of inertia of a body about a given axis is 1.2 kg m
2
.
Initially, the body is at rest. In order to produce a rotational kinetic
energy of 1500 joule, an angular acceleration of 25  radian/sec
2
 must be
applied about that axis for a duration of
(a) 4 seconds
(b) 2 seconds
(c) 8 seconds
(d) 10 seconds
2. A pulley of radius 2 m is rotated about its axis by a force F = (20t – 5t
2
)
newton (where t is measured in seconds) applied tangentially. If the
moment of inertia of the pulley about its axis of rotation is 10 kg-m
2
 the
number of rotations made by the pulley before its direction of motion is
reversed, is:
(a) more than 3 but less than 6
(b) more than 6 but less than 9
(c) more than 9
(d) less than 3
3. A gymnast takes turns with her arms and legs stretched. When she pulls
her arms and legs in
(a) the angular velocity decreases
(b) the moment of inertia decreases
(c) the angular velocity stays constant
(d) the angular momentum increases
4. An equilateral triangle ABC formed from a uniform
wire has two small identical beads initially located at
A. The triangle is set rotating about the vertical axis AO. Then the beads
are released from rest simultaneously and
allowed to slide down, one along AB and the other along AC as shown.
Neglecting frictional effects, the quantities that are conserved as the
beads slide down, are
(a) angular velocity and total energy (kinetic and potential)
(b) total angular momentum and total energy
(c) angular velocity and moment of inertia about the axis of rotation
(d) total angular momentum and moment of inertia about the axis of rotation
5. Two identical discs of mass m and radius r are arranged as shown in the
figure. If a is the angular acceleration of the lower disc and a
cm
 is
acceleration of centre of mass of the lower disc, then relation between
a
cm
,
a and r is
(a) a
cm
 = a/r
(b) a
cm
 = 2ar
(c) a
cm
 = a r
(d) None of these
6. A tennis ball (treated as hollow spherical shell) starting
from O rolls down a hill. At point A the ball becomes air borne leaving
at an angle of 30° with the horizontal. The ball strikes the ground at B.
What is the value of the distance AB ?
(Moment of inertia of a spherical shell of mass m and radius R about its
diameter 
(a) 1.87 m
(b) 2.08 m
(c) 1.57 m
(d) 1.77 m
7. A hollow sphere is held suspended. Sand is now
poured into it in stages.
The centre of mass of the sphere with
the sand
(a) rises continuously
(b) remains unchanged in the process
(c) first rises and then falls to the
original position
(d) first falls and then rises to the original position
8. From a solid sphere of mass M and radius R a cube of maximum
possible volume is cut. Moment of inertia of cube about an axis passing
through its center and perpendicular to one of its faces is :
(a)
(b)
(c)
(d)
9. A solid sphere is rolling on a surface as shown in figure, with a
translational velocity v m s
–1
. If it is to climb the inclined surface
continuing to roll without slipping, then minimum velocity for this to
happen is
(a)
(b)
(c)
(d)
10. A loop of radius r and mass m rotating with an
angular velocity ?
0
 is placed on a rough
horizontal surface. The initial velocity of the centre of the hoop is
zero.What will be the velocity of the centre of the hoop when it ceases
to slip?
(a)
(b)
(c)
(d) r?
0
11. A thin rod of length ‘L’ is lying along the x-axis with its ends at x = 0
and x = L. Its linear density 
(mass/length) varies with x as ,
where n can be zero or any positive number. If the position x
CM
 of the
centre of mass of the rod is plotted against ‘n’, which of the following
graphs best approximates the dependence of x
CM
 on n?
(a)
(b)
(c)
(d)
12. A mass m moves in a circle on a smooth horizontal plane with velocity
v
0
 at a radius R
0
. The mass is attached to  string which passes through a
smooth hole in the plane as shown.
The tension in the string is increased gradually and
finally m moves in a circle of radius . The
final value of the kinetic energy is
(a)
(b)
(c)
(d)
13. 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