Rotational Motion– 1 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 thin circular ring of mass M and radius  r is rotating
about its  axis with a constant angular velocity w. 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
M 4m
w
+
(b)
( ) M 4m
M
+w
   (c) 
( ) M 4m
M 4m
-w
+
    (d)   
M
4m
w
Q..2 The angular momentum of a system of particles is
conserved
(a) When no external force acts upon the system
(b) When no external torque acts upon the system
(c) When no external impulse acts upon the system
(d) When axis of rotation remains same
Q.3 Two rigid bodies A and B rotate with rotational kinetic
energies E
A
 and E
B
 respectively. The moments of inertia
of A and B about the axis of rotation are I
A
 and I
B
 respectively .
If I
A
 = I
B
/4 and E
A
 = 100 E
B
, the ratio of angular momentum
(L
A
) of A to the angular momentum (L
B
) of B is
(a) 25 (b) 5/4 (c)5 (d) 1/4
Q.4 A uniform heavy disc is rotating at constant angular velocity
w about a vertical axis through its centre and perpendicular
to the plane of the disc. Let L be its angular momentum. A
lump of plasticine is dropped vertically on the disc and
sticks to it. Which of the following will be constant?
(a) w (b) w and L both
(c) L only (d) Neither w nor L
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 thin circular ring of mass M and radius  r is rotating
about its  axis with a constant angular velocity w. 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
M 4m
w
+
(b)
( ) M 4m
M
+w
   (c) 
( ) M 4m
M 4m
-w
+
    (d)   
M
4m
w
Q..2 The angular momentum of a system of particles is
conserved
(a) When no external force acts upon the system
(b) When no external torque acts upon the system
(c) When no external impulse acts upon the system
(d) When axis of rotation remains same
Q.3 Two rigid bodies A and B rotate with rotational kinetic
energies E
A
 and E
B
 respectively. The moments of inertia
of A and B about the axis of rotation are I
A
 and I
B
 respectively .
If I
A
 = I
B
/4 and E
A
 = 100 E
B
, the ratio of angular momentum
(L
A
) of A to the angular momentum (L
B
) of B is
(a) 25 (b) 5/4 (c)5 (d) 1/4
Q.4 A uniform heavy disc is rotating at constant angular velocity
w about a vertical axis through its centre and perpendicular
to the plane of the disc. Let L be its angular momentum. A
lump of plasticine is dropped vertically on the disc and
sticks to it. Which of the following will be constant?
(a) w (b) w and L both
(c) L only (d) Neither w nor L
2
DPP/ P 15
Q.5 Two discs of  moment of inertia I
1
 and I
2
 and angular speeds
w
1
 and w
2
 are rotating along collinear axes passing through
their centre of mass and perpendicular  to their  plane. If
the  two are made to rotate combindly along the same axis
the rotational KE of system will be
(a)
( )
1 1 22
12
II
2II
w +w
+
(b)
( )( )
2
1 2 12
II
2
+ w +w
(c)
( )
( )
2
1 1 22
12
II
2II
w +w
+
(d) None of these
Q.6 A particle performs uniform circular  motion with an
angular momentum L. If the frequency of a particle's
motion is doubled  and its kinetic energy is halved, the
angular momentum becomes.
(a) 2 L (b) 4 L (c) L/2 (d) L/4
Q.7 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 w about the same axis. The final
angular velocity of the combination of discs is
(a)
2
12
I
II
w
+
(b) w (c)
1
12
I
II
w
+
(d)
( )
12
1
II
I
+w
Q.8 Calculate the angular momentum of a body whose rotational
energy is 10 joule. If the angular momentum vector
coincides with the axis of rotation and its moment of inertia
about this  axis is 8×10
-7
 kg m
2
(a) 4 × 10
–3  
kg m
2 
/s (b) 2 × 10
–3
 kg m
2
/s
(c) 6 × 10
–3
 kg m
2
/s (d) None of these
Q.9 If  the earth is treated as a sphere of radius R and mass M. Its
angular momentum about the axis of rotation with period T
is
(a)
3
MR
T
p
(b)
2
MR
T
p
(c)
2
2 MR
5T
p
(d)
2
4 MR
5T
p
Q.10 If the earth is a point mass of 6×10
24
kg  revolving around
the sun at a distance of 1.5×10
8
 km and in time T = 3.14
×10
7
s. then the  angular momentum of the earth around
the sun is
(a) 1.2 × 10
18
 kg m
2
/s (b) 1.8 × 10
29
 kg m
2
/s
(c) 1.5 × 10
37
 kg m
2
/s (d) 2.7 × 10
40
 kg m
2
/s
Q.11 An automobile engine develops 100 kW when rotating at a
speed of 1800 rev/min. What torque does it deliver
(a) 350 N-m (b) 440 N-m
(c) 531 N-m (d) 628 N-m
Q.12A constant  torque  acting on a uniform circular wheel
changes its angular momentum from A
0
 to 4A
0
 in 4 seconds.
The magnitude  of this torque is
(a)
0
3A
4
(b)A
0
(c) 4A
0
(d) 12A
0
Q.13A wheel having moment of inertia 2 kg -m
2
 about its
vertical axis, rotates at the rate of 60 rpm about this axis.
The torque which can stop the wheel's rotation in 1 minute
would be
(a)
2
Nm
15
p
(b) Nm
12
p
(c) Nm
15
p
(d) Nm
18
p
Q.14 Find the torque of a force F 3i j 5k
r Ù ÙÙ
=- ++ acting  at the
point r 7i 3jk
r Ù ÙÙ
= ++
(a)
14 i 38 j 16k
Ù ÙÙ
-+
(b)
4 i 4 j 6k
Ù ÙÙ
++
(c)
14 i 38 j 16 k
Ù ÙÙ
- +-
(d)
21i 3 j 5k
Ù ÙÙ
- ++
Q.15 A constant torque of 1000 N -m, turns a wheel of moment
of inertia 200 kg -m
2
 about an axis passing through the
centre. Angular velocity of the wheel after 3 s will be
(a) 15 rad/s (b) 10 rad/s (c) 5 rad/s (d) 1 rad/s
Q.16A torque of 30 N-m is applied on a 5 kg wheel whose
moment of inertia is 2kg-m
2
 for 10 sec. The angle covered
by the wheel in 10 sec will be
(a) 750 rad (b) 1500 rad
(c) 3000 rad (d) 6000 rad
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 thin circular ring of mass M and radius  r is rotating
about its  axis with a constant angular velocity w. 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
M 4m
w
+
(b)
( ) M 4m
M
+w
   (c) 
( ) M 4m
M 4m
-w
+
    (d)   
M
4m
w
Q..2 The angular momentum of a system of particles is
conserved
(a) When no external force acts upon the system
(b) When no external torque acts upon the system
(c) When no external impulse acts upon the system
(d) When axis of rotation remains same
Q.3 Two rigid bodies A and B rotate with rotational kinetic
energies E
A
 and E
B
 respectively. The moments of inertia
of A and B about the axis of rotation are I
A
 and I
B
 respectively .
If I
A
 = I
B
/4 and E
A
 = 100 E
B
, the ratio of angular momentum
(L
A
) of A to the angular momentum (L
B
) of B is
(a) 25 (b) 5/4 (c)5 (d) 1/4
Q.4 A uniform heavy disc is rotating at constant angular velocity
w about a vertical axis through its centre and perpendicular
to the plane of the disc. Let L be its angular momentum. A
lump of plasticine is dropped vertically on the disc and
sticks to it. Which of the following will be constant?
(a) w (b) w and L both
(c) L only (d) Neither w nor L
2
DPP/ P 15
Q.5 Two discs of  moment of inertia I
1
 and I
2
 and angular speeds
w
1
 and w
2
 are rotating along collinear axes passing through
their centre of mass and perpendicular  to their  plane. If
the  two are made to rotate combindly along the same axis
the rotational KE of system will be
(a)
( )
1 1 22
12
II
2II
w +w
+
(b)
( )( )
2
1 2 12
II
2
+ w +w
(c)
( )
( )
2
1 1 22
12
II
2II
w +w
+
(d) None of these
Q.6 A particle performs uniform circular  motion with an
angular momentum L. If the frequency of a particle's
motion is doubled  and its kinetic energy is halved, the
angular momentum becomes.
(a) 2 L (b) 4 L (c) L/2 (d) L/4
Q.7 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 w about the same axis. The final
angular velocity of the combination of discs is
(a)
2
12
I
II
w
+
(b) w (c)
1
12
I
II
w
+
(d)
( )
12
1
II
I
+w
Q.8 Calculate the angular momentum of a body whose rotational
energy is 10 joule. If the angular momentum vector
coincides with the axis of rotation and its moment of inertia
about this  axis is 8×10
-7
 kg m
2
(a) 4 × 10
–3  
kg m
2 
/s (b) 2 × 10
–3
 kg m
2
/s
(c) 6 × 10
–3
 kg m
2
/s (d) None of these
Q.9 If  the earth is treated as a sphere of radius R and mass M. Its
angular momentum about the axis of rotation with period T
is
(a)
3
MR
T
p
(b)
2
MR
T
p
(c)
2
2 MR
5T
p
(d)
2
4 MR
5T
p
Q.10 If the earth is a point mass of 6×10
24
kg  revolving around
the sun at a distance of 1.5×10
8
 km and in time T = 3.14
×10
7
s. then the  angular momentum of the earth around
the sun is
(a) 1.2 × 10
18
 kg m
2
/s (b) 1.8 × 10
29
 kg m
2
/s
(c) 1.5 × 10
37
 kg m
2
/s (d) 2.7 × 10
40
 kg m
2
/s
Q.11 An automobile engine develops 100 kW when rotating at a
speed of 1800 rev/min. What torque does it deliver
(a) 350 N-m (b) 440 N-m
(c) 531 N-m (d) 628 N-m
Q.12A constant  torque  acting on a uniform circular wheel
changes its angular momentum from A
0
 to 4A
0
 in 4 seconds.
The magnitude  of this torque is
(a)
0
3A
4
(b)A
0
(c) 4A
0
(d) 12A
0
Q.13A wheel having moment of inertia 2 kg -m
2
 about its
vertical axis, rotates at the rate of 60 rpm about this axis.
The torque which can stop the wheel's rotation in 1 minute
would be
(a)
2
Nm
15
p
(b) Nm
12
p
(c) Nm
15
p
(d) Nm
18
p
Q.14 Find the torque of a force F 3i j 5k
r Ù ÙÙ
=- ++ acting  at the
point r 7i 3jk
r Ù ÙÙ
= ++
(a)
14 i 38 j 16k
Ù ÙÙ
-+
(b)
4 i 4 j 6k
Ù ÙÙ
++
(c)
14 i 38 j 16 k
Ù ÙÙ
- +-
(d)
21i 3 j 5k
Ù ÙÙ
- ++
Q.15 A constant torque of 1000 N -m, turns a wheel of moment
of inertia 200 kg -m
2
 about an axis passing through the
centre. Angular velocity of the wheel after 3 s will be
(a) 15 rad/s (b) 10 rad/s (c) 5 rad/s (d) 1 rad/s
Q.16A torque of 30 N-m is applied on a 5 kg wheel whose
moment of inertia is 2kg-m
2
 for 10 sec. The angle covered
by the wheel in 10 sec will be
(a) 750 rad (b) 1500 rad
(c) 3000 rad (d) 6000 rad
DPP/ P 15
3
Q.17 A horizontal force F is applied such that the block remains
stationary , then which of the following statement is false
a
a
F
(a) f = mg [where f is the friction force]
(b) F = N [ where N is the normal reaction]
(c) F will not produce torque
(d) N will not produce torque
Q.18 In a bicycle, the radius of rear wheel is twice the radius of
front wheel. If r
F
 and r
r
 are the radius, v
F
 and v
r
 are speeds
of top most points of wheel, then
(a)v
r
 = 2 v
F
(b)v
F
 = 2 v
r
(c)v
F
 = v
r
(d)v
F
 > v
r
Q.19 The wheel of a car is rotating at the rate of 1200 revolutions
per minute. On pressing the accelerator for 10 seconds, it
starts rotating at 4500 revolutions per minute. The angular
acceleration of the wheel is
(a) 30 rad/sec
2
(b) 1880 degree/sec
2
(c) 40 rad/sec
2
(d) 1980 degree/sec
2
Q.20 A wheel rotates with a constant acceleration of 2.0 radian/
sec
2
. It the wheel  starts from rest, the number of
revolutions it makes in the first ten seconds will be
approximately
(a)8 (b) 16 (c) 24 (d) 32
DIRECTIONS (Q.21-Q.22) : 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.21A child is standing with folded hands at the centre of a
platform rotating about its central axis. The kinetic energy
of the system is K. The child now stretches his arms so
that the moment of inertia of the system doubles. The
kinetic energy of the system now is
(1) less than 2K (2) equal to K/2
(3) more thanK/4 (4) equal to 4K
Q.22Two uniforms discs of equal mass but unequal radii are
mounted on fixed horizontal axiles. Light strings are
wrapped on each of the discs. The strings are pulled by
constant equal forces F for same amount of time as shown
in the figure.
F
Disc I
Disc II
F
Angular momenta of discs are L
1
 and L
2
 and their kinetic
energies are K
1
 and K
2
. Which of the following statements
true –
(1) L
1
 = L
2
(2) L
1
 < L
2
(3) K
1
 > K
2
(4) K
1
 = K
2
DIRECTIONS (Q.23-Q.25) : Read the passage given below
and answer the questions that follows :
Consider a cylinder of mass M = 1kg and radius R = 1 m lying on
a rough horizontal plane. It has a plank lying on its top as shown in
the figure.
F
B
R
A 
60°  
m = 1kg
M
A force F = 55 N is applied on the plank such that the
plank moves and causes the cylinder to roll. The plank
always remains horizontal. There is no slipping at any
point of contact.
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 thin circular ring of mass M and radius  r is rotating
about its  axis with a constant angular velocity w. 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
M 4m
w
+
(b)
( ) M 4m
M
+w
   (c) 
( ) M 4m
M 4m
-w
+
    (d)   
M
4m
w
Q..2 The angular momentum of a system of particles is
conserved
(a) When no external force acts upon the system
(b) When no external torque acts upon the system
(c) When no external impulse acts upon the system
(d) When axis of rotation remains same
Q.3 Two rigid bodies A and B rotate with rotational kinetic
energies E
A
 and E
B
 respectively. The moments of inertia
of A and B about the axis of rotation are I
A
 and I
B
 respectively .
If I
A
 = I
B
/4 and E
A
 = 100 E
B
, the ratio of angular momentum
(L
A
) of A to the angular momentum (L
B
) of B is
(a) 25 (b) 5/4 (c)5 (d) 1/4
Q.4 A uniform heavy disc is rotating at constant angular velocity
w about a vertical axis through its centre and perpendicular
to the plane of the disc. Let L be its angular momentum. A
lump of plasticine is dropped vertically on the disc and
sticks to it. Which of the following will be constant?
(a) w (b) w and L both
(c) L only (d) Neither w nor L
2
DPP/ P 15
Q.5 Two discs of  moment of inertia I
1
 and I
2
 and angular speeds
w
1
 and w
2
 are rotating along collinear axes passing through
their centre of mass and perpendicular  to their  plane. If
the  two are made to rotate combindly along the same axis
the rotational KE of system will be
(a)
( )
1 1 22
12
II
2II
w +w
+
(b)
( )( )
2
1 2 12
II
2
+ w +w
(c)
( )
( )
2
1 1 22
12
II
2II
w +w
+
(d) None of these
Q.6 A particle performs uniform circular  motion with an
angular momentum L. If the frequency of a particle's
motion is doubled  and its kinetic energy is halved, the
angular momentum becomes.
(a) 2 L (b) 4 L (c) L/2 (d) L/4
Q.7 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 w about the same axis. The final
angular velocity of the combination of discs is
(a)
2
12
I
II
w
+
(b) w (c)
1
12
I
II
w
+
(d)
( )
12
1
II
I
+w
Q.8 Calculate the angular momentum of a body whose rotational
energy is 10 joule. If the angular momentum vector
coincides with the axis of rotation and its moment of inertia
about this  axis is 8×10
-7
 kg m
2
(a) 4 × 10
–3  
kg m
2 
/s (b) 2 × 10
–3
 kg m
2
/s
(c) 6 × 10
–3
 kg m
2
/s (d) None of these
Q.9 If  the earth is treated as a sphere of radius R and mass M. Its
angular momentum about the axis of rotation with period T
is
(a)
3
MR
T
p
(b)
2
MR
T
p
(c)
2
2 MR
5T
p
(d)
2
4 MR
5T
p
Q.10 If the earth is a point mass of 6×10
24
kg  revolving around
the sun at a distance of 1.5×10
8
 km and in time T = 3.14
×10
7
s. then the  angular momentum of the earth around
the sun is
(a) 1.2 × 10
18
 kg m
2
/s (b) 1.8 × 10
29
 kg m
2
/s
(c) 1.5 × 10
37
 kg m
2
/s (d) 2.7 × 10
40
 kg m
2
/s
Q.11 An automobile engine develops 100 kW when rotating at a
speed of 1800 rev/min. What torque does it deliver
(a) 350 N-m (b) 440 N-m
(c) 531 N-m (d) 628 N-m
Q.12A constant  torque  acting on a uniform circular wheel
changes its angular momentum from A
0
 to 4A
0
 in 4 seconds.
The magnitude  of this torque is
(a)
0
3A
4
(b)A
0
(c) 4A
0
(d) 12A
0
Q.13A wheel having moment of inertia 2 kg -m
2
 about its
vertical axis, rotates at the rate of 60 rpm about this axis.
The torque which can stop the wheel's rotation in 1 minute
would be
(a)
2
Nm
15
p
(b) Nm
12
p
(c) Nm
15
p
(d) Nm
18
p
Q.14 Find the torque of a force F 3i j 5k
r Ù ÙÙ
=- ++ acting  at the
point r 7i 3jk
r Ù ÙÙ
= ++
(a)
14 i 38 j 16k
Ù ÙÙ
-+
(b)
4 i 4 j 6k
Ù ÙÙ
++
(c)
14 i 38 j 16 k
Ù ÙÙ
- +-
(d)
21i 3 j 5k
Ù ÙÙ
- ++
Q.15 A constant torque of 1000 N -m, turns a wheel of moment
of inertia 200 kg -m
2
 about an axis passing through the
centre. Angular velocity of the wheel after 3 s will be
(a) 15 rad/s (b) 10 rad/s (c) 5 rad/s (d) 1 rad/s
Q.16A torque of 30 N-m is applied on a 5 kg wheel whose
moment of inertia is 2kg-m
2
 for 10 sec. The angle covered
by the wheel in 10 sec will be
(a) 750 rad (b) 1500 rad
(c) 3000 rad (d) 6000 rad
DPP/ P 15
3
Q.17 A horizontal force F is applied such that the block remains
stationary , then which of the following statement is false
a
a
F
(a) f = mg [where f is the friction force]
(b) F = N [ where N is the normal reaction]
(c) F will not produce torque
(d) N will not produce torque
Q.18 In a bicycle, the radius of rear wheel is twice the radius of
front wheel. If r
F
 and r
r
 are the radius, v
F
 and v
r
 are speeds
of top most points of wheel, then
(a)v
r
 = 2 v
F
(b)v
F
 = 2 v
r
(c)v
F
 = v
r
(d)v
F
 > v
r
Q.19 The wheel of a car is rotating at the rate of 1200 revolutions
per minute. On pressing the accelerator for 10 seconds, it
starts rotating at 4500 revolutions per minute. The angular
acceleration of the wheel is
(a) 30 rad/sec
2
(b) 1880 degree/sec
2
(c) 40 rad/sec
2
(d) 1980 degree/sec
2
Q.20 A wheel rotates with a constant acceleration of 2.0 radian/
sec
2
. It the wheel  starts from rest, the number of
revolutions it makes in the first ten seconds will be
approximately
(a)8 (b) 16 (c) 24 (d) 32
DIRECTIONS (Q.21-Q.22) : 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.21A child is standing with folded hands at the centre of a
platform rotating about its central axis. The kinetic energy
of the system is K. The child now stretches his arms so
that the moment of inertia of the system doubles. The
kinetic energy of the system now is
(1) less than 2K (2) equal to K/2
(3) more thanK/4 (4) equal to 4K
Q.22Two uniforms discs of equal mass but unequal radii are
mounted on fixed horizontal axiles. Light strings are
wrapped on each of the discs. The strings are pulled by
constant equal forces F for same amount of time as shown
in the figure.
F
Disc I
Disc II
F
Angular momenta of discs are L
1
 and L
2
 and their kinetic
energies are K
1
 and K
2
. Which of the following statements
true –
(1) L
1
 = L
2
(2) L
1
 < L
2
(3) K
1
 > K
2
(4) K
1
 = K
2
DIRECTIONS (Q.23-Q.25) : Read the passage given below
and answer the questions that follows :
Consider a cylinder of mass M = 1kg and radius R = 1 m lying on
a rough horizontal plane. It has a plank lying on its top as shown in
the figure.
F
B
R
A 
60°  
m = 1kg
M
A force F = 55 N is applied on the plank such that the
plank moves and causes the cylinder to roll. The plank
always remains horizontal. There is no slipping at any
point of contact.
4
DPP/ P 15
Q.23 Calculate the acceleration of cylinder.
(a) 20 m/s
2
(b) 10 m/s
2
(c) 5 m/s
2
(d) None of these
Q.24 Find the value of frictional force at A
(a) 7.5 N (b) 5.0 N
(c) 2.5 N (d) None of these
Q.25 Find the value of frictional force at B
(a) 7.5 N (b) 5.0 N
(c) 2.5 N (d)  None of these
DIRECTIONS (Q.26-Q.28) : 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.26 Statement -1: Torque is equal to rate of change of angular
momentum.
Statement -2: Angular momentum depends on moment
of  inertia and angular velocity .
Q.27 Statement -1: Torque due to force is maximum when angle
between r
r
 and F
r
 is 90°.
Statement -2: The unit of torque is newton- meter.
Q.28 Statement -1: It is harder to open and shut the door if we
apply force near the hinge.
Statement -2: Torque is maximum at hinge of the door.