Rotational Motion- 2 Practice Questions - DPP for NEET

 Page 1


DIRECTIONS (Q.1-Q.21) : There are 21 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 Five particles of mass 2 kg are attached to the rim of a
circular disc of radius 0.1 m & negligible mass. Moment
of inertia of the system about an axis passing through the
centre of the disc & perpendicular to its plane is
(a) 1 kg-m
2
(b) 0.1kg-m
2
(c)  2 kg-m
2
(d) 0.2 kg-m
2
Q.2 Two discs of the same material and thickness have radii 0.2
m and 0.6 m. Their moments of inertia about their axes will
be in the ratio of
(a) 1 : 81 (b) 1: 27 (c) 1 : 9 (d) 1 : 3
Q.3 A cylinder of 500 g and radius 10 cm has moment of inertia
(about its natural axis)
(a) 2.5 × 10
–3
 kg–m
2
(b) 2 × 10
–3
 kg–m
2
(c) 5 × 10
–3
 kg–m
2
(d) 3.5 × 10
–3 
kg–m
2
Q.4 A constant torque of 31.4 N–m is exerted on a pivoted
wheel. If angular acceleration of wheel is 4p rad/sec
2
, then
the moment of inertia of the wheel is
(a) 2.5 kg–m
2
(b) 2.5 kg–m
2
(c) 4.5 kg–m
2
(d) 5.5 kg–m
2
Q.5 From a uniform wire, two circular loops are made (i) P of
radius r and (ii) Q of radius nr. If the moment of inertia of
loop Q about an axis passing through its centre and
perpendicular to its plane is 8 times that of P about a similar
axis, the value of n is (diameter of the wire is very much
smaller than r or nr)
(a)8 (b)6
(c)4 (d)2
Page 2


DIRECTIONS (Q.1-Q.21) : There are 21 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 Five particles of mass 2 kg are attached to the rim of a
circular disc of radius 0.1 m & negligible mass. Moment
of inertia of the system about an axis passing through the
centre of the disc & perpendicular to its plane is
(a) 1 kg-m
2
(b) 0.1kg-m
2
(c)  2 kg-m
2
(d) 0.2 kg-m
2
Q.2 Two discs of the same material and thickness have radii 0.2
m and 0.6 m. Their moments of inertia about their axes will
be in the ratio of
(a) 1 : 81 (b) 1: 27 (c) 1 : 9 (d) 1 : 3
Q.3 A cylinder of 500 g and radius 10 cm has moment of inertia
(about its natural axis)
(a) 2.5 × 10
–3
 kg–m
2
(b) 2 × 10
–3
 kg–m
2
(c) 5 × 10
–3
 kg–m
2
(d) 3.5 × 10
–3 
kg–m
2
Q.4 A constant torque of 31.4 N–m is exerted on a pivoted
wheel. If angular acceleration of wheel is 4p rad/sec
2
, then
the moment of inertia of the wheel is
(a) 2.5 kg–m
2
(b) 2.5 kg–m
2
(c) 4.5 kg–m
2
(d) 5.5 kg–m
2
Q.5 From a uniform wire, two circular loops are made (i) P of
radius r and (ii) Q of radius nr. If the moment of inertia of
loop Q about an axis passing through its centre and
perpendicular to its plane is 8 times that of P about a similar
axis, the value of n is (diameter of the wire is very much
smaller than r or nr)
(a)8 (b)6
(c)4 (d)2
2
DPP/ P 16
Q.6 The moment of inertia of a sphere of mass M and radius R
ab o u t an axis passing thro ug h its c e ntre is 
2
2
MR
5
. The radius
of gyration of the sphere about a parallel axis to the above
and tangent to the sphere is
(a)
7
R
5
(b)
3
R
5
(c)
7
R
5
æö
÷ ç
÷
ç
÷
ç
÷
÷ ç
èø
(d)
3
R
5
æö
÷ ç
÷ ç
÷
ç
÷
÷ ç
èø
Q.7 Four particles each of mass m are placed at the corners of
a square of side length l. The radius of gyration of the
system about an axis perpendicular to the square and
passing through its centre is
(a)
2
l
(b)
2
l
(c) l (d) ( 2) l
Q.8 The radius of gyration of a disc of mass 50 g and radius 2.5
cm, about an axis passing through its centre of gravity and
perpendicular to the plane is
(a) 0.52 cm (b) 1.76 cm (c) 3.54 cm (d) 6.54 cm
Q.9 Moment of inertia of a ring of mass m = 3 gm and radius
r = 1 cm about an axis passing through its edge and parallel
to its natural axis is
(a) 10 gm–cm
2
(b) 100 gm–cm
2
(c) 6 gm–cm
2
(d) 1 gm–cm
2
Q.10 A disc is of mass M and radius r. The moment of inertia of
it about an axis tangential to its edge and in plane of the
disc or parallel to its diameter is
(a)
2
5
Mr
4
(b)
2
Mr
4
(c)
2
3
Mr
2
(d)
2
Mr
2
Q.11 Two spheres each of mass M and radius R/2 are connected
with a massless rod of length 2R as shown in the figure.
M
R/2
M
R/2
2R
The moment of inertia
of the system about an
axis passing through
the centre of one of the
spheres and
perpendicular to the
rod will be
(a)
2
21
Mr
5
(b)
2
2
Mr
5
(c)
2
5
Mr
2
(d)
2
5
Mr
21
Q.12 Three point masses m
1
, m
2
, m
3
 are located at the vertices
of an equilateral triangle of length 'a'. The moment of
inertia of the system about an axis along the altitude of the
triangle passing through m
1
, is
(a) (m
2
 + m
3
) 
2
a
4
(b) (m
1
 + m
2
 + m
3
) a
2
(c) (m
1
 + m
2
) 
2
a
4
(d) (m
2
 + m
3
) a
2
Q.13 Three rods each of length L and mass M are placed along
X, Y and Z axis in such a way that one end of each of the
rod is at the origin. The moment of inertia of this system
about Z axis is
(a)
2
2ML
3
(b)
2
4ML
3
(c)
2
5ML
3
(d)
2
ML
3
Q.14 ABC is a triangular plate of uniform
thickness. The sides are in the ratio
shown in the figure. I
AB
, I
BC
, I
CA
 are
the moments of inertia of the plate
about AB, BC, CA respectively. For
this arrangement which one of the
following relation is correct?
B C
A        
5 4
3
(a)I
CA
 is maximum (b)I
BC
 > I
AB
(c)I
BC
 > I
AB
(d)I
AB
 + I
BC
 = I
CA
Q.15 A 1m long rod has a mass of 0.12 kg. The moment of inertia
about an axis passin through the centre and perpendicular
to the length of rod will be
(a) 0.01kg-m
2
(b) 0.001 kg-m
2
(c) 1 kg-m
2
(d) 10 kg-m
2
Q.16 Two rings of the same radius and mass are placed such that
their centres are at a common point and their planes are
perpendicular to each other. The moment of inertia of the
system about an axis passing through the centre and
perpendicular to the plane of one of the rings is (mass of
the ring = m and radius = r)
(a)
2
1
2
mr (b) mr
2
(c)
2
3
2
mr (d) 2 mr
2
Page 3


DIRECTIONS (Q.1-Q.21) : There are 21 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 Five particles of mass 2 kg are attached to the rim of a
circular disc of radius 0.1 m & negligible mass. Moment
of inertia of the system about an axis passing through the
centre of the disc & perpendicular to its plane is
(a) 1 kg-m
2
(b) 0.1kg-m
2
(c)  2 kg-m
2
(d) 0.2 kg-m
2
Q.2 Two discs of the same material and thickness have radii 0.2
m and 0.6 m. Their moments of inertia about their axes will
be in the ratio of
(a) 1 : 81 (b) 1: 27 (c) 1 : 9 (d) 1 : 3
Q.3 A cylinder of 500 g and radius 10 cm has moment of inertia
(about its natural axis)
(a) 2.5 × 10
–3
 kg–m
2
(b) 2 × 10
–3
 kg–m
2
(c) 5 × 10
–3
 kg–m
2
(d) 3.5 × 10
–3 
kg–m
2
Q.4 A constant torque of 31.4 N–m is exerted on a pivoted
wheel. If angular acceleration of wheel is 4p rad/sec
2
, then
the moment of inertia of the wheel is
(a) 2.5 kg–m
2
(b) 2.5 kg–m
2
(c) 4.5 kg–m
2
(d) 5.5 kg–m
2
Q.5 From a uniform wire, two circular loops are made (i) P of
radius r and (ii) Q of radius nr. If the moment of inertia of
loop Q about an axis passing through its centre and
perpendicular to its plane is 8 times that of P about a similar
axis, the value of n is (diameter of the wire is very much
smaller than r or nr)
(a)8 (b)6
(c)4 (d)2
2
DPP/ P 16
Q.6 The moment of inertia of a sphere of mass M and radius R
ab o u t an axis passing thro ug h its c e ntre is 
2
2
MR
5
. The radius
of gyration of the sphere about a parallel axis to the above
and tangent to the sphere is
(a)
7
R
5
(b)
3
R
5
(c)
7
R
5
æö
÷ ç
÷
ç
÷
ç
÷
÷ ç
èø
(d)
3
R
5
æö
÷ ç
÷ ç
÷
ç
÷
÷ ç
èø
Q.7 Four particles each of mass m are placed at the corners of
a square of side length l. The radius of gyration of the
system about an axis perpendicular to the square and
passing through its centre is
(a)
2
l
(b)
2
l
(c) l (d) ( 2) l
Q.8 The radius of gyration of a disc of mass 50 g and radius 2.5
cm, about an axis passing through its centre of gravity and
perpendicular to the plane is
(a) 0.52 cm (b) 1.76 cm (c) 3.54 cm (d) 6.54 cm
Q.9 Moment of inertia of a ring of mass m = 3 gm and radius
r = 1 cm about an axis passing through its edge and parallel
to its natural axis is
(a) 10 gm–cm
2
(b) 100 gm–cm
2
(c) 6 gm–cm
2
(d) 1 gm–cm
2
Q.10 A disc is of mass M and radius r. The moment of inertia of
it about an axis tangential to its edge and in plane of the
disc or parallel to its diameter is
(a)
2
5
Mr
4
(b)
2
Mr
4
(c)
2
3
Mr
2
(d)
2
Mr
2
Q.11 Two spheres each of mass M and radius R/2 are connected
with a massless rod of length 2R as shown in the figure.
M
R/2
M
R/2
2R
The moment of inertia
of the system about an
axis passing through
the centre of one of the
spheres and
perpendicular to the
rod will be
(a)
2
21
Mr
5
(b)
2
2
Mr
5
(c)
2
5
Mr
2
(d)
2
5
Mr
21
Q.12 Three point masses m
1
, m
2
, m
3
 are located at the vertices
of an equilateral triangle of length 'a'. The moment of
inertia of the system about an axis along the altitude of the
triangle passing through m
1
, is
(a) (m
2
 + m
3
) 
2
a
4
(b) (m
1
 + m
2
 + m
3
) a
2
(c) (m
1
 + m
2
) 
2
a
4
(d) (m
2
 + m
3
) a
2
Q.13 Three rods each of length L and mass M are placed along
X, Y and Z axis in such a way that one end of each of the
rod is at the origin. The moment of inertia of this system
about Z axis is
(a)
2
2ML
3
(b)
2
4ML
3
(c)
2
5ML
3
(d)
2
ML
3
Q.14 ABC is a triangular plate of uniform
thickness. The sides are in the ratio
shown in the figure. I
AB
, I
BC
, I
CA
 are
the moments of inertia of the plate
about AB, BC, CA respectively. For
this arrangement which one of the
following relation is correct?
B C
A        
5 4
3
(a)I
CA
 is maximum (b)I
BC
 > I
AB
(c)I
BC
 > I
AB
(d)I
AB
 + I
BC
 = I
CA
Q.15 A 1m long rod has a mass of 0.12 kg. The moment of inertia
about an axis passin through the centre and perpendicular
to the length of rod will be
(a) 0.01kg-m
2
(b) 0.001 kg-m
2
(c) 1 kg-m
2
(d) 10 kg-m
2
Q.16 Two rings of the same radius and mass are placed such that
their centres are at a common point and their planes are
perpendicular to each other. The moment of inertia of the
system about an axis passing through the centre and
perpendicular to the plane of one of the rings is (mass of
the ring = m and radius = r)
(a)
2
1
2
mr (b) mr
2
(c)
2
3
2
mr (d) 2 mr
2
DPP/ P 16
3
Q.17 One quarter sector is cut from a uniform
circular disc of radius R. This sector has
mass M. It is made to rotate about a line
perpendicular to its plane and passing
through the centre of the original disc.
Its moment of inertia about the axis of
rotation is
90°
(a)
2
1
2
MR (b)
2
1
4
MR (c)
2
1
8
MR (d)
2
2MR
Q.18 A thin wire of length L and uniform linear mass density r is
bent into a circular loop with centre at O as shown in figure.
The moment of inertia of the loop about the axis XX¢ is
(a)
3
2
8
L r
p
(b)
3
2
16
L r
p
(c)
3
2
5
16
L r
p
X X¢
90°
O
(d)
3
2
3
8
L r
p
Q.19 Two disc of same thickness but of different radii are made
of two different materials such that their masses are same.
The densities of the materials are in the ratio 1 : 3. The
ratio of the moments of inertia of these discs about the
respective axes passing through their centres and
perpendicular to their planes will be in
(a) 1 : 3 (b) 3 : 1 (c) 1 : 9 (d) 9 : 1
Q.20 A circular disc of radius R and thickness 
6
R
 has moment
of inertia I about an axis passing through its centre and
perpendicular to its plane. It is melted and recasted into a
solid sphere. The moment of inertia of the sphere about
one of its diameter as an axis of rotation will be
(a)I (b)
2
8
I
(c)
5
I
(d)
10
I
Q.21 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) 3 MR
2
(b)
2
3
MR
2
Y
Y¢
(c) 5 MR
2
(d)
2
7
MR
2
DIRECTIONS (Q.22-Q.24) : 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.22 The density of a rod AB increases linearly from A to B. Its
midpoint is O and its centre of mass is at C. Four axes pass
through A, B, O and C, all perpendicular to the length of
the rod. The moments of inertia of the rod about these
a xe s a re I
A
, I
B
, I
O
 and I
C
 respectively then:.
(1) I
A
 > I
B
(2) I
A
 < I
B
(3) I
O
 > I
C
(4) I
O
 < I
C
Q.23The moment of inertia of a thin square plate ABCD of
uniform thickness about an axis passing through the centre
O and perpendicular to the plane of the plate is
3
C
A
D
O
B
2
1
4
(1) I
1
 + I
2
(2) I
3
 + I
4
(3) I
1
 + I
3
(4) I
1
 + I
2
 + I
3
 + I
4
where I
1
, I
2
, I
3
 and I
4
 are
respectively moments of
inertia about axes 1, 2, 3 and
4 which are in the plane of the
plate.
Q.24 Moment of inertia doesn’t depend on
(1) distribution of particles
(2) mass
(3) position of axis of rotation
(4) None of these
Page 4


DIRECTIONS (Q.1-Q.21) : There are 21 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONLY ONE choice is correct.
Q.1 Five particles of mass 2 kg are attached to the rim of a
circular disc of radius 0.1 m & negligible mass. Moment
of inertia of the system about an axis passing through the
centre of the disc & perpendicular to its plane is
(a) 1 kg-m
2
(b) 0.1kg-m
2
(c)  2 kg-m
2
(d) 0.2 kg-m
2
Q.2 Two discs of the same material and thickness have radii 0.2
m and 0.6 m. Their moments of inertia about their axes will
be in the ratio of
(a) 1 : 81 (b) 1: 27 (c) 1 : 9 (d) 1 : 3
Q.3 A cylinder of 500 g and radius 10 cm has moment of inertia
(about its natural axis)
(a) 2.5 × 10
–3
 kg–m
2
(b) 2 × 10
–3
 kg–m
2
(c) 5 × 10
–3
 kg–m
2
(d) 3.5 × 10
–3 
kg–m
2
Q.4 A constant torque of 31.4 N–m is exerted on a pivoted
wheel. If angular acceleration of wheel is 4p rad/sec
2
, then
the moment of inertia of the wheel is
(a) 2.5 kg–m
2
(b) 2.5 kg–m
2
(c) 4.5 kg–m
2
(d) 5.5 kg–m
2
Q.5 From a uniform wire, two circular loops are made (i) P of
radius r and (ii) Q of radius nr. If the moment of inertia of
loop Q about an axis passing through its centre and
perpendicular to its plane is 8 times that of P about a similar
axis, the value of n is (diameter of the wire is very much
smaller than r or nr)
(a)8 (b)6
(c)4 (d)2
2
DPP/ P 16
Q.6 The moment of inertia of a sphere of mass M and radius R
ab o u t an axis passing thro ug h its c e ntre is 
2
2
MR
5
. The radius
of gyration of the sphere about a parallel axis to the above
and tangent to the sphere is
(a)
7
R
5
(b)
3
R
5
(c)
7
R
5
æö
÷ ç
÷
ç
÷
ç
÷
÷ ç
èø
(d)
3
R
5
æö
÷ ç
÷ ç
÷
ç
÷
÷ ç
èø
Q.7 Four particles each of mass m are placed at the corners of
a square of side length l. The radius of gyration of the
system about an axis perpendicular to the square and
passing through its centre is
(a)
2
l
(b)
2
l
(c) l (d) ( 2) l
Q.8 The radius of gyration of a disc of mass 50 g and radius 2.5
cm, about an axis passing through its centre of gravity and
perpendicular to the plane is
(a) 0.52 cm (b) 1.76 cm (c) 3.54 cm (d) 6.54 cm
Q.9 Moment of inertia of a ring of mass m = 3 gm and radius
r = 1 cm about an axis passing through its edge and parallel
to its natural axis is
(a) 10 gm–cm
2
(b) 100 gm–cm
2
(c) 6 gm–cm
2
(d) 1 gm–cm
2
Q.10 A disc is of mass M and radius r. The moment of inertia of
it about an axis tangential to its edge and in plane of the
disc or parallel to its diameter is
(a)
2
5
Mr
4
(b)
2
Mr
4
(c)
2
3
Mr
2
(d)
2
Mr
2
Q.11 Two spheres each of mass M and radius R/2 are connected
with a massless rod of length 2R as shown in the figure.
M
R/2
M
R/2
2R
The moment of inertia
of the system about an
axis passing through
the centre of one of the
spheres and
perpendicular to the
rod will be
(a)
2
21
Mr
5
(b)
2
2
Mr
5
(c)
2
5
Mr
2
(d)
2
5
Mr
21
Q.12 Three point masses m
1
, m
2
, m
3
 are located at the vertices
of an equilateral triangle of length 'a'. The moment of
inertia of the system about an axis along the altitude of the
triangle passing through m
1
, is
(a) (m
2
 + m
3
) 
2
a
4
(b) (m
1
 + m
2
 + m
3
) a
2
(c) (m
1
 + m
2
) 
2
a
4
(d) (m
2
 + m
3
) a
2
Q.13 Three rods each of length L and mass M are placed along
X, Y and Z axis in such a way that one end of each of the
rod is at the origin. The moment of inertia of this system
about Z axis is
(a)
2
2ML
3
(b)
2
4ML
3
(c)
2
5ML
3
(d)
2
ML
3
Q.14 ABC is a triangular plate of uniform
thickness. The sides are in the ratio
shown in the figure. I
AB
, I
BC
, I
CA
 are
the moments of inertia of the plate
about AB, BC, CA respectively. For
this arrangement which one of the
following relation is correct?
B C
A        
5 4
3
(a)I
CA
 is maximum (b)I
BC
 > I
AB
(c)I
BC
 > I
AB
(d)I
AB
 + I
BC
 = I
CA
Q.15 A 1m long rod has a mass of 0.12 kg. The moment of inertia
about an axis passin through the centre and perpendicular
to the length of rod will be
(a) 0.01kg-m
2
(b) 0.001 kg-m
2
(c) 1 kg-m
2
(d) 10 kg-m
2
Q.16 Two rings of the same radius and mass are placed such that
their centres are at a common point and their planes are
perpendicular to each other. The moment of inertia of the
system about an axis passing through the centre and
perpendicular to the plane of one of the rings is (mass of
the ring = m and radius = r)
(a)
2
1
2
mr (b) mr
2
(c)
2
3
2
mr (d) 2 mr
2
DPP/ P 16
3
Q.17 One quarter sector is cut from a uniform
circular disc of radius R. This sector has
mass M. It is made to rotate about a line
perpendicular to its plane and passing
through the centre of the original disc.
Its moment of inertia about the axis of
rotation is
90°
(a)
2
1
2
MR (b)
2
1
4
MR (c)
2
1
8
MR (d)
2
2MR
Q.18 A thin wire of length L and uniform linear mass density r is
bent into a circular loop with centre at O as shown in figure.
The moment of inertia of the loop about the axis XX¢ is
(a)
3
2
8
L r
p
(b)
3
2
16
L r
p
(c)
3
2
5
16
L r
p
X X¢
90°
O
(d)
3
2
3
8
L r
p
Q.19 Two disc of same thickness but of different radii are made
of two different materials such that their masses are same.
The densities of the materials are in the ratio 1 : 3. The
ratio of the moments of inertia of these discs about the
respective axes passing through their centres and
perpendicular to their planes will be in
(a) 1 : 3 (b) 3 : 1 (c) 1 : 9 (d) 9 : 1
Q.20 A circular disc of radius R and thickness 
6
R
 has moment
of inertia I about an axis passing through its centre and
perpendicular to its plane. It is melted and recasted into a
solid sphere. The moment of inertia of the sphere about
one of its diameter as an axis of rotation will be
(a)I (b)
2
8
I
(c)
5
I
(d)
10
I
Q.21 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) 3 MR
2
(b)
2
3
MR
2
Y
Y¢
(c) 5 MR
2
(d)
2
7
MR
2
DIRECTIONS (Q.22-Q.24) : 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.22 The density of a rod AB increases linearly from A to B. Its
midpoint is O and its centre of mass is at C. Four axes pass
through A, B, O and C, all perpendicular to the length of
the rod. The moments of inertia of the rod about these
a xe s a re I
A
, I
B
, I
O
 and I
C
 respectively then:.
(1) I
A
 > I
B
(2) I
A
 < I
B
(3) I
O
 > I
C
(4) I
O
 < I
C
Q.23The moment of inertia of a thin square plate ABCD of
uniform thickness about an axis passing through the centre
O and perpendicular to the plane of the plate is
3
C
A
D
O
B
2
1
4
(1) I
1
 + I
2
(2) I
3
 + I
4
(3) I
1
 + I
3
(4) I
1
 + I
2
 + I
3
 + I
4
where I
1
, I
2
, I
3
 and I
4
 are
respectively moments of
inertia about axes 1, 2, 3 and
4 which are in the plane of the
plate.
Q.24 Moment of inertia doesn’t depend on
(1) distribution of particles
(2) mass
(3) position of axis of rotation
(4) None of these
4
DPP/ P 16
DIRECTIONS (Q.25-Q.27) : Read the passage given below
and answer the questions that follows :
Four identical spheres having mass M and
radius R are fixed tightly within a massless ring
such that the centres of all spheres lie in the
plane of ring. The ring is kept on a rough
horizontal table as shown. The string is wrapped
around the ring can roll without slipping.
The other end of the string is passed over a massless frictionless
pulley to a block of mass M. A force F is applied horizontally on
the ring, at the same level as the centre, so that the system is in
equilibrium.
Q.25 The moment of inertia of the combined ring system about
the centre of ring will be
(a)
2
12
5
MR
(b)
2
48
15
MR
M
F
(c)
2
24
5
MR
(d)
2
48
5
MR
Q.26 The magnitude of F is
(a) Mg (b)2Mg
(c)
g
2
M
(d) None of these
Q.27If the masses of the spheres were doubled keeping their
dimensions same, the force of friction between the ring
and the horizontal surface would
(a) be doubled
(b) increase but be less than double
(c) remain the same
(d) decrease
DIRECTIONS (Q. 28-Q.30) : 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.28 Statement-1 : Radius of gyration of a body is a constant
quantity.
Statement-2 : The radius of gyration of a body about an
axis of rotation may be defined as the root mean square
distance of the particles of the body from the axis of rotation.
Q.29Statement-1 : Moment of inertia of a particle is same,
whatever be the axis of rotation.
Statement-2 : Moment of inertia depends on mass and
perpendicular distance of the particle from its axis of
rotation.
Q.30 Statement-1 : If earth shrink (without change in mass) to
half of its present size, length of the day would become 6
hours.
Statement-2 : When the size of the earth will change, its
moment of inertia will also change.