Rotational Motion - 3 Practice Questions - DPP for NEET

 Page 1


DIRECTIONS (Q.1-Q.20) : There are 20 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 A disc is rolling (without slipping) on a horizontal surface. C is
its centre and Q and P are two points equidistant from C . Let v
P
,
v
Q
 and v
C
  be the magnitude of velocities of points P , Q and
C respectively, then
(a)
>>
Q CP
vvv
(b)
<<
Q CP
v vv
(c)
,
2
P
Q PC
v
v vv ==
P
C
Q
(d)
<>
Q CP
v vv
Q.2 A uniform rod of length 2L  is placed with one end in contact
with the horizontal and is then inclined at an angle a to the
horizontal and allowed to fall without slipping at contact
point. When it becomes horizontal, its angular velocity will
be
(a)
3 sin
2
g
L
a
w=
(b)
2
3 sin
L
g
w=
a
(c)
6 sin g
L
a
w=
(d)
sin
L
g
w=
a
Page 2


DIRECTIONS (Q.1-Q.20) : There are 20 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 A disc is rolling (without slipping) on a horizontal surface. C is
its centre and Q and P are two points equidistant from C . Let v
P
,
v
Q
 and v
C
  be the magnitude of velocities of points P , Q and
C respectively, then
(a)
>>
Q CP
vvv
(b)
<<
Q CP
v vv
(c)
,
2
P
Q PC
v
v vv ==
P
C
Q
(d)
<>
Q CP
v vv
Q.2 A uniform rod of length 2L  is placed with one end in contact
with the horizontal and is then inclined at an angle a to the
horizontal and allowed to fall without slipping at contact
point. When it becomes horizontal, its angular velocity will
be
(a)
3 sin
2
g
L
a
w=
(b)
2
3 sin
L
g
w=
a
(c)
6 sin g
L
a
w=
(d)
sin
L
g
w=
a
2
DPP/ P 17
Q.3 According to the theorem of parallel axes 
2
cm
=+ I I Mx,
the graph between I and x will be
(a)
O
I
x
(b)
O
I
x
(c)
O
I
x
(d)
O
I
x
Q.4 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)
3
4
gh (b)
4
3
gh (c) 4gh (d) 2gh
Q.5 An inclined plane makes an angle 30° with the horizontal.
A solid sphere rolling down this inclined plane from rest
without slipping has a linear acceleration equal to
(a)
3
g
(b)
2
3
g
(c)
5
7
g
(d)
5
14
g
Q.6 A cord is wound round the circumference of wheel of radius
r. The axis of the wheel is horizontal and moment of inertia
about it is I. A weight mg is attached to the end of the cord
and falls from the rest. After falling through a distance h,
the angular velocity of the wheel will be
(a)
2
+
gh
I mr
(b)
1/2
2
2éù
êú
+ëû
mgh
I mr
(c)
1/2
2
2
2
éù
êú
+ëû
mgh
I mr
(d) 2gh
Q.7 A solid sphere, disc and solid cylinder all of the same mass
and made up of same material are allowed to roll down
(from rest) on an inclined plane, then
(a) Solid sphere reaches the bottom first
(b) Solid sphere reaches the bottom late
(c) Disc will reach the bottom first
(d) All of them reach the bottom at the same time
Q.8 A solid sphere is rolling on a frictionless surface, shown
in figure with a transnational velocity v m/s. If sphere climbs
up to height h then value of v should be
v
h
(a)
10
7
gh ³
(b) 2gh ³ (c) 2gh (d)
10
7
gh
Q.9 Moment of inertia of a disc about its own axis is I. Its
moment of inertia about a tangential axis in its plane is
(a)
5
2
I (b)
3I
(c)
3
2
I (d)
2I
Q.10 Three rings each of mass M and radius R are arranged as
shown in the figure. The moment of inertia of the system
about YY' will be
(a)
2
3MR
(b)
2
3
2
MR
Y
' Y
(c)
2
5MR
(d)
2
7
2
MR
Q.11 One circular ring and one circular disc, both are having the
same mass and radius. The ratio of their moments of inertia
about the axes passing through their centres and perpendicular
to their planes, will be
(a) 1 : 1 (b) 2 : 1
(c) 1 : 2 (d) 4 : 1
Q.12From a disc of radius R, a concentric circular portion of
radius r is cut out so as to leave an annular disc of mass M.
The moment of inertia of this annular disc about the axis
perpendicular to its plane and passing through its centre of
gravity is
(a)
22
1
()
2
MRr + (b)
22
1
()
2
MRr -
(c)
44
1
()
2
MRr + (d)
44
1
()
2
MRr -
Page 3


DIRECTIONS (Q.1-Q.20) : There are 20 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 A disc is rolling (without slipping) on a horizontal surface. C is
its centre and Q and P are two points equidistant from C . Let v
P
,
v
Q
 and v
C
  be the magnitude of velocities of points P , Q and
C respectively, then
(a)
>>
Q CP
vvv
(b)
<<
Q CP
v vv
(c)
,
2
P
Q PC
v
v vv ==
P
C
Q
(d)
<>
Q CP
v vv
Q.2 A uniform rod of length 2L  is placed with one end in contact
with the horizontal and is then inclined at an angle a to the
horizontal and allowed to fall without slipping at contact
point. When it becomes horizontal, its angular velocity will
be
(a)
3 sin
2
g
L
a
w=
(b)
2
3 sin
L
g
w=
a
(c)
6 sin g
L
a
w=
(d)
sin
L
g
w=
a
2
DPP/ P 17
Q.3 According to the theorem of parallel axes 
2
cm
=+ I I Mx,
the graph between I and x will be
(a)
O
I
x
(b)
O
I
x
(c)
O
I
x
(d)
O
I
x
Q.4 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)
3
4
gh (b)
4
3
gh (c) 4gh (d) 2gh
Q.5 An inclined plane makes an angle 30° with the horizontal.
A solid sphere rolling down this inclined plane from rest
without slipping has a linear acceleration equal to
(a)
3
g
(b)
2
3
g
(c)
5
7
g
(d)
5
14
g
Q.6 A cord is wound round the circumference of wheel of radius
r. The axis of the wheel is horizontal and moment of inertia
about it is I. A weight mg is attached to the end of the cord
and falls from the rest. After falling through a distance h,
the angular velocity of the wheel will be
(a)
2
+
gh
I mr
(b)
1/2
2
2éù
êú
+ëû
mgh
I mr
(c)
1/2
2
2
2
éù
êú
+ëû
mgh
I mr
(d) 2gh
Q.7 A solid sphere, disc and solid cylinder all of the same mass
and made up of same material are allowed to roll down
(from rest) on an inclined plane, then
(a) Solid sphere reaches the bottom first
(b) Solid sphere reaches the bottom late
(c) Disc will reach the bottom first
(d) All of them reach the bottom at the same time
Q.8 A solid sphere is rolling on a frictionless surface, shown
in figure with a transnational velocity v m/s. If sphere climbs
up to height h then value of v should be
v
h
(a)
10
7
gh ³
(b) 2gh ³ (c) 2gh (d)
10
7
gh
Q.9 Moment of inertia of a disc about its own axis is I. Its
moment of inertia about a tangential axis in its plane is
(a)
5
2
I (b)
3I
(c)
3
2
I (d)
2I
Q.10 Three rings each of mass M and radius R are arranged as
shown in the figure. The moment of inertia of the system
about YY' will be
(a)
2
3MR
(b)
2
3
2
MR
Y
' Y
(c)
2
5MR
(d)
2
7
2
MR
Q.11 One circular ring and one circular disc, both are having the
same mass and radius. The ratio of their moments of inertia
about the axes passing through their centres and perpendicular
to their planes, will be
(a) 1 : 1 (b) 2 : 1
(c) 1 : 2 (d) 4 : 1
Q.12From a disc of radius R, a concentric circular portion of
radius r is cut out so as to leave an annular disc of mass M.
The moment of inertia of this annular disc about the axis
perpendicular to its plane and passing through its centre of
gravity is
(a)
22
1
()
2
MRr + (b)
22
1
()
2
MRr -
(c)
44
1
()
2
MRr + (d)
44
1
()
2
MRr -
DPP/ P 17
3
Q.13 The moment of inertia of a straight thin rod of mass M and
length l about an axis perpendicular to its length and passing
through its one end, is
(a)
2
M
12
l
(b)
2
M
3
l
(c)
2
M
2
l
(d) Ml
2
Q.14 Four thin rods of same mass M and same length l, form a
square as shown in figure. Moment of inertia of this
system about an axis through centre
O and perpendicular to its plane is
(a)
2
4
3
Ml
(b)
2
3
Ml
O
l
l
l
l
(c)
2
6
Ml
(d)
2
2
3
Ml
Q.15 The moment of inertia of a uniform circular ring, having a
mass M and a radius R, about an axis tangential to the ring
and perpendicular to its plane, is
(a)
2
2MR (b)
2
3
2
MR (c)
2
1
2
MR (d)
2
MR
Q.16 The moment of inertia of uniform rectangular plate about an
axis passing through its mid-point and parallel to its length
l is (b = breadth of rectangular plate)
(a)
2
4
Mb
(b)
3
6
Mb
(c)
3
12
Mb
(d)
2
12
Mb
Q.17 The moment of inertia of a circular ring about an axis passing
through its centre and normal to its plane is 200 gm × cm
2
.
Then  moment of inertia about its diameter is
(a) 400 gm × cm
2
(b) 300 gm × cm
2
(c) 200 gm × cm
2
(d) 100 gm × cm
2
Q.18 From a circular disc of radius R and mass 9 M, a small disc of
radius R/3 is removed from the disc. The moment of inertia of
the remaining disc about an axis perpendicular to the plane of
the disc and passing through O is
(a) 4MR
2
(b)
40
9
MR
2
O
R
2 /3 R
(c)
2
10MR
(d)
37
9
MR
2
Q.19 The moment of inertia of a thin rod of mass M and length L
about an axis perpendicular to the rod at a distance L/4 from
one end is
(a)
2
6
ML
(b)
2
12
ML
(c)
2
7
24
ML
(d)
2
7
48
ML
Q.20 A wheel has a speed of 1200 revolutions per minute  and is
made to slow down at a rate of 4 radians /s
2
. The number of
revolutions it makes before coming to rest is
(a) 143 (b) 272 (c) 314 (d) 722
DIRECTIONS (Q.21-Q.23) : In the following questions,
more than one of the answers  given are correct. Select
the correct answers and mark it according to the following
codes:
Codes:
(a) 1, 2 and 3 are correct (b) 1 and 2 are correct
(c) 2 and 4 are correct (d) 1 and 3 are correct
Q.21 In pure rolling fraction of its total energy associated with
rotation is a for a ring and b for a solid sphere. Then
(1) 1/2 a= (2) 2/7 b= (3) 2/5 b= (4) 1/4 a=
Q.22 One solid sphere and a disc of same radius are falling along
an inclined plane without slip. One reaches earlier than the
other due to
(1) different size
(2) different radius of gyration
(3) different moment of inertia
(4) different friction
Q.23 A body is rolling down an inclined plane. Its translational
and rotational kinetic energies are equal. The body is not a
(1) solid sphere (2) hollow sphere
(3) solid cylinder (4) hollow cylinder
Page 4


DIRECTIONS (Q.1-Q.20) : There are 20 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 A disc is rolling (without slipping) on a horizontal surface. C is
its centre and Q and P are two points equidistant from C . Let v
P
,
v
Q
 and v
C
  be the magnitude of velocities of points P , Q and
C respectively, then
(a)
>>
Q CP
vvv
(b)
<<
Q CP
v vv
(c)
,
2
P
Q PC
v
v vv ==
P
C
Q
(d)
<>
Q CP
v vv
Q.2 A uniform rod of length 2L  is placed with one end in contact
with the horizontal and is then inclined at an angle a to the
horizontal and allowed to fall without slipping at contact
point. When it becomes horizontal, its angular velocity will
be
(a)
3 sin
2
g
L
a
w=
(b)
2
3 sin
L
g
w=
a
(c)
6 sin g
L
a
w=
(d)
sin
L
g
w=
a
2
DPP/ P 17
Q.3 According to the theorem of parallel axes 
2
cm
=+ I I Mx,
the graph between I and x will be
(a)
O
I
x
(b)
O
I
x
(c)
O
I
x
(d)
O
I
x
Q.4 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)
3
4
gh (b)
4
3
gh (c) 4gh (d) 2gh
Q.5 An inclined plane makes an angle 30° with the horizontal.
A solid sphere rolling down this inclined plane from rest
without slipping has a linear acceleration equal to
(a)
3
g
(b)
2
3
g
(c)
5
7
g
(d)
5
14
g
Q.6 A cord is wound round the circumference of wheel of radius
r. The axis of the wheel is horizontal and moment of inertia
about it is I. A weight mg is attached to the end of the cord
and falls from the rest. After falling through a distance h,
the angular velocity of the wheel will be
(a)
2
+
gh
I mr
(b)
1/2
2
2éù
êú
+ëû
mgh
I mr
(c)
1/2
2
2
2
éù
êú
+ëû
mgh
I mr
(d) 2gh
Q.7 A solid sphere, disc and solid cylinder all of the same mass
and made up of same material are allowed to roll down
(from rest) on an inclined plane, then
(a) Solid sphere reaches the bottom first
(b) Solid sphere reaches the bottom late
(c) Disc will reach the bottom first
(d) All of them reach the bottom at the same time
Q.8 A solid sphere is rolling on a frictionless surface, shown
in figure with a transnational velocity v m/s. If sphere climbs
up to height h then value of v should be
v
h
(a)
10
7
gh ³
(b) 2gh ³ (c) 2gh (d)
10
7
gh
Q.9 Moment of inertia of a disc about its own axis is I. Its
moment of inertia about a tangential axis in its plane is
(a)
5
2
I (b)
3I
(c)
3
2
I (d)
2I
Q.10 Three rings each of mass M and radius R are arranged as
shown in the figure. The moment of inertia of the system
about YY' will be
(a)
2
3MR
(b)
2
3
2
MR
Y
' Y
(c)
2
5MR
(d)
2
7
2
MR
Q.11 One circular ring and one circular disc, both are having the
same mass and radius. The ratio of their moments of inertia
about the axes passing through their centres and perpendicular
to their planes, will be
(a) 1 : 1 (b) 2 : 1
(c) 1 : 2 (d) 4 : 1
Q.12From a disc of radius R, a concentric circular portion of
radius r is cut out so as to leave an annular disc of mass M.
The moment of inertia of this annular disc about the axis
perpendicular to its plane and passing through its centre of
gravity is
(a)
22
1
()
2
MRr + (b)
22
1
()
2
MRr -
(c)
44
1
()
2
MRr + (d)
44
1
()
2
MRr -
DPP/ P 17
3
Q.13 The moment of inertia of a straight thin rod of mass M and
length l about an axis perpendicular to its length and passing
through its one end, is
(a)
2
M
12
l
(b)
2
M
3
l
(c)
2
M
2
l
(d) Ml
2
Q.14 Four thin rods of same mass M and same length l, form a
square as shown in figure. Moment of inertia of this
system about an axis through centre
O and perpendicular to its plane is
(a)
2
4
3
Ml
(b)
2
3
Ml
O
l
l
l
l
(c)
2
6
Ml
(d)
2
2
3
Ml
Q.15 The moment of inertia of a uniform circular ring, having a
mass M and a radius R, about an axis tangential to the ring
and perpendicular to its plane, is
(a)
2
2MR (b)
2
3
2
MR (c)
2
1
2
MR (d)
2
MR
Q.16 The moment of inertia of uniform rectangular plate about an
axis passing through its mid-point and parallel to its length
l is (b = breadth of rectangular plate)
(a)
2
4
Mb
(b)
3
6
Mb
(c)
3
12
Mb
(d)
2
12
Mb
Q.17 The moment of inertia of a circular ring about an axis passing
through its centre and normal to its plane is 200 gm × cm
2
.
Then  moment of inertia about its diameter is
(a) 400 gm × cm
2
(b) 300 gm × cm
2
(c) 200 gm × cm
2
(d) 100 gm × cm
2
Q.18 From a circular disc of radius R and mass 9 M, a small disc of
radius R/3 is removed from the disc. The moment of inertia of
the remaining disc about an axis perpendicular to the plane of
the disc and passing through O is
(a) 4MR
2
(b)
40
9
MR
2
O
R
2 /3 R
(c)
2
10MR
(d)
37
9
MR
2
Q.19 The moment of inertia of a thin rod of mass M and length L
about an axis perpendicular to the rod at a distance L/4 from
one end is
(a)
2
6
ML
(b)
2
12
ML
(c)
2
7
24
ML
(d)
2
7
48
ML
Q.20 A wheel has a speed of 1200 revolutions per minute  and is
made to slow down at a rate of 4 radians /s
2
. The number of
revolutions it makes before coming to rest is
(a) 143 (b) 272 (c) 314 (d) 722
DIRECTIONS (Q.21-Q.23) : In the following questions,
more than one of the answers  given are correct. Select
the correct answers and mark it according to the following
codes:
Codes:
(a) 1, 2 and 3 are correct (b) 1 and 2 are correct
(c) 2 and 4 are correct (d) 1 and 3 are correct
Q.21 In pure rolling fraction of its total energy associated with
rotation is a for a ring and b for a solid sphere. Then
(1) 1/2 a= (2) 2/7 b= (3) 2/5 b= (4) 1/4 a=
Q.22 One solid sphere and a disc of same radius are falling along
an inclined plane without slip. One reaches earlier than the
other due to
(1) different size
(2) different radius of gyration
(3) different moment of inertia
(4) different friction
Q.23 A body is rolling down an inclined plane. Its translational
and rotational kinetic energies are equal. The body is not a
(1) solid sphere (2) hollow sphere
(3) solid cylinder (4) hollow cylinder
4
DPP/ P 17
Space for Rough Work
DIRECTIONS (Q.24-Q.26) : Read the passage given below and
answer the questions that follows :
A uniform solid cylinder of mass 2m and
radius R rolls on a rough inclined plane
with its axis perpendicular to the line of
the greatest slope.
 ////////////////////////// ////////////////
m
2m
R
q
System is released from rest and as
the cylinder rolls it winds up a light
string which passes over a light pul-
ley.
Q.24 The acceleration of block of mass m is -
(a)
2
g(1 cos)
7
-q (b)
4
g(1 sin)
7
-q
(c)
2
g(1 sin)
7
-q (d)
2
g(1 sin)
14
+q
Q.25 The tension in the string is –
(a)
4 3sin
mg
7
+q æö
ç÷
èø
(b)
3 4sin
mg
7
-q æö
ç÷
èø
(c)
3 4sin
mg
7
+q æö
ç÷
èø
(d)
2
(1 sin ) mg
7
-q
Q.26 The frictional force acting on the cylinder is-
(a)
2
(1 sin ) mg
7
-q (b)
6 sin
mg
7
-q æö
ç÷
èø
(c)
1 6cos
mg
7
+q æö
ç÷
èø
(d)
1 6sin
mg
7
+q æö
ç÷
èø
DIRECTIONS (Q. 27-Q.29) : Each of these questions contains
two statements: Statement-1 (Assertion) and Statement-2
(Reason). Each of these questions has four alternative choices,
only one of which is the correct answer. You have to select
the correct choice.
(a) Statement-1 is True, Statement-2 is True; Statement-2 is a
correct explanation for  Statement-1.
(b) Statement-1 is True, Statement-2 is True; Statement-2 is
NOT a correct explanation for Statement-1.
(c) Statement -1 is False, Statement-2 is True.
(d) Statement -1 is True, Statement-2 is False.
Q.27 Statement-1 : Two cylinders, one hollow (metal) and the
other solid (wood) with the same mass and identical
dimensions are simultaneously allowed to roll without
slipping down an inclined plane from the same height. The
hollow cylinder will reach the bottom of the inclined plane
first.
Statement-2 : By the principle of conservation of energy,
the total kinetic energies of both the cylinders are identical
when they reach the bottom of the incline.
Q.28 Statement-1: The force of frction in the case of a disc
rolling without slipping down an inclined plane is 1/3 g
sin a.
Statement-2: When the disc rolls without slipping, friction
is required because for rolling condition velocity of point
of contact is zero.
Q.29 Statement-1: If two different axes are at same distance
from the centre of mass of a rigid body, then moment of
inertia of the given rigid body about both the axes will
always be the same.
Statement-2: From parallel axis theorem, I = I
cm
 + md 
2
,
where all terms have usual meaning.
24. 25. 26. 27. 28.
29.
RESPONSE
GRID
Total Questions 29 Total Marks 116
Attempted Correct
Incorrect Net Score
Cut-off Score 28 Qualifying Score 44
DAILY PRACTICE PROBLEM SHEET 17 - PHYSICS
Success Gap = Net Score – Qualifying Score
Net Score = (Correct × 4) – (Incorrect × 1)
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