Centre of Mass and its Motion 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 In  the HCl molecule, the separation between the nuclei of
the two atom is about 1.27 A° (1A° = 10
–10
 m). The
approximate location of the centre of mass from the
hydrogen atom, assuming the chlorine atom to be about
35.5 times massive as hydrogen is
(a) 1 Å (b) 2.5 Å (c) 1.24 Å (d) 1.5 Å
Q.2 A 2 kg body and a 3 kg body are moving along the x-axis. A t
a particular instant the 2 kg bo dy has a velocity of 3 ms
–1
 and the
3 kg body has the velocity of 2ms
–1
. The velocity of the
centre of mass at that instant is
(a) 5 ms
–1
(b) 1 ms
–1
(c)0 (d) None of these
Q.3 The distance between the carbon atom and the oxygen atom
in a carbon monoxide molecule is 1.1 Å. Given, mass of
carbon atom is 12 a.m.u. and mass of oxygen atom is 16
a.m.u., calculate the position of the centre of mass of the
carbon monoxide molecule
(a) 6.3 Å from the carbon atom
(b) 1 Å from the oxygen atom
(c) 0.63 Å from the carbon atom
(d) 0.12 Å from the oxygen atom
Q.4 The velocities of three particles of masses 20g, 30g and
50g are 
ˆ ˆˆ
10 ,10 and10 i jk respectively. The velocity of the
centre of mass of the three particles is
(a)
ˆ ˆˆ
2 3 +5 i jk + (b) 
ˆ ˆˆ
10( +) i jk +
(c)
ˆ ˆˆ
20 30 +5 i jk + (d) 
ˆ ˆˆ
2 30 +50 i jk +
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 In  the HCl molecule, the separation between the nuclei of
the two atom is about 1.27 A° (1A° = 10
–10
 m). The
approximate location of the centre of mass from the
hydrogen atom, assuming the chlorine atom to be about
35.5 times massive as hydrogen is
(a) 1 Å (b) 2.5 Å (c) 1.24 Å (d) 1.5 Å
Q.2 A 2 kg body and a 3 kg body are moving along the x-axis. A t
a particular instant the 2 kg bo dy has a velocity of 3 ms
–1
 and the
3 kg body has the velocity of 2ms
–1
. The velocity of the
centre of mass at that instant is
(a) 5 ms
–1
(b) 1 ms
–1
(c)0 (d) None of these
Q.3 The distance between the carbon atom and the oxygen atom
in a carbon monoxide molecule is 1.1 Å. Given, mass of
carbon atom is 12 a.m.u. and mass of oxygen atom is 16
a.m.u., calculate the position of the centre of mass of the
carbon monoxide molecule
(a) 6.3 Å from the carbon atom
(b) 1 Å from the oxygen atom
(c) 0.63 Å from the carbon atom
(d) 0.12 Å from the oxygen atom
Q.4 The velocities of three particles of masses 20g, 30g and
50g are 
ˆ ˆˆ
10 ,10 and10 i jk respectively. The velocity of the
centre of mass of the three particles is
(a)
ˆ ˆˆ
2 3 +5 i jk + (b) 
ˆ ˆˆ
10( +) i jk +
(c)
ˆ ˆˆ
20 30 +5 i jk + (d) 
ˆ ˆˆ
2 30 +50 i jk +
2
DPP/ P 14
Q.5 The centre of mass of a triangle shown in figure has
coordinates
(a)
hb
x= ,y
22
=
(b)
bh
x ,y
22
==
h
b
x
y
(c)
bh
x ,y
33
==
(d)
hb
x ,y
33
==
Q.6 Two bodies of masses 2 kg and 4 kg are moving with
velocities 2 m/s and 10 m/s respectively along same
direction. Then the velocity of their centre of mass will be
(a) 8.1 m/s (b) 7.3 m/s
(c) 6.4 m/s (d) 5.3 m/s
Q.7 Four particles of masses m, 2m, 3m and 4m are arranged at
the corners of a parallelogram with each side equal to a
and one of the angle between two adjacent sides is 60°.
The parallelogram lies in the x-y plane with mass m at the
origin and 4m on the x-axis. The centre of mass of the
arrangement will be located at
(a)
3
,0.95
2
aa
æö
ç÷
èø
(b)
3
0.95 ,
4
aa
æö
ç÷
èø
(c)
3
,
42
aa æö
ç÷
èø
(d)
3
,
24
aa æö
ç÷
èø
Q.8 Three identical metal balls each of radius r are placed touching
each other on a horizontal surface such that an equilateral
triangle is formed, when centres of three balls are joined.
The centre of the mass of system is located at
(a) Horizontal surface
(b) Centre of one of the balls
(c) Line joining centres of any two balls
(d) Point of intersection of the medians
Q.9 2 bodies of different masses of 2 kg and 4 kg are moving
with velocities 20 m/s and 10 m/s towards each other due
to mutual gravitational attraction. What is the velocity of
their centre of mass?
(a) 5 m/s (b) 6 m/s
(c) 8 m/s (d) Zero
Q.10 Two particles of masses m
1
 and m
2
  initially at rest start
moving towards each other under their mutual force of
attraction. The speed of the centre  of mass at any time t,
when they are at a distance r apart, is
(a) zero (b) 
12
2
1
1
.
mm
Gt
m
r
æö
ç÷
èø
(c)
12
2
2
1
.
mm
Gt
m
r
æö
ç÷
èø
(d) 
12
2
12
1
.
mm
Gt
mm
r
æö
ç÷
+ èø
Q.11 A 'T' shaped object,  dimensions shown in the figure, is
lying on a smooth floor. A force 'F'
r
 is applied at the point
P parallel to AB, such that the object has only the
translational motion without rotation. Find the location of
P with respect to C
(a)
4
3
l
(b) I
(c)
2
3
l                                             
l
B
2l
A
P
C
F
(d)
3
2
l
Q.12 Two spheres of masses 2M and M are initially at rest at a
distance R apart. Due to mutual force of attraction, they
approach each other. When they are at separation R/2, the
acceleration of the centre of mass of spheres would be
(a) 0 m/s
2
(b) g m/s
2
(c) 3 g m/s
2
(d) 12 g m/s
2
Q.13 Masses 8 kg, 2 kg, 4 kg and 2 kg are placed at the corners
A, B, C, D respectively of a square ABCD of diagonal 80
cm. The distance of centre of mass from A will be
(a) 20 cm (b) 30 cm
(c) 40 cm (d) 60 cm
Q.14 If linear density of a rod of length 3m varies as l = 2 + x,
them the position of the centre of gravity of the rod is
(a)
7
m
3
(b)
12
m
7
(c)
10
m
7
(d)
9
m
7
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 In  the HCl molecule, the separation between the nuclei of
the two atom is about 1.27 A° (1A° = 10
–10
 m). The
approximate location of the centre of mass from the
hydrogen atom, assuming the chlorine atom to be about
35.5 times massive as hydrogen is
(a) 1 Å (b) 2.5 Å (c) 1.24 Å (d) 1.5 Å
Q.2 A 2 kg body and a 3 kg body are moving along the x-axis. A t
a particular instant the 2 kg bo dy has a velocity of 3 ms
–1
 and the
3 kg body has the velocity of 2ms
–1
. The velocity of the
centre of mass at that instant is
(a) 5 ms
–1
(b) 1 ms
–1
(c)0 (d) None of these
Q.3 The distance between the carbon atom and the oxygen atom
in a carbon monoxide molecule is 1.1 Å. Given, mass of
carbon atom is 12 a.m.u. and mass of oxygen atom is 16
a.m.u., calculate the position of the centre of mass of the
carbon monoxide molecule
(a) 6.3 Å from the carbon atom
(b) 1 Å from the oxygen atom
(c) 0.63 Å from the carbon atom
(d) 0.12 Å from the oxygen atom
Q.4 The velocities of three particles of masses 20g, 30g and
50g are 
ˆ ˆˆ
10 ,10 and10 i jk respectively. The velocity of the
centre of mass of the three particles is
(a)
ˆ ˆˆ
2 3 +5 i jk + (b) 
ˆ ˆˆ
10( +) i jk +
(c)
ˆ ˆˆ
20 30 +5 i jk + (d) 
ˆ ˆˆ
2 30 +50 i jk +
2
DPP/ P 14
Q.5 The centre of mass of a triangle shown in figure has
coordinates
(a)
hb
x= ,y
22
=
(b)
bh
x ,y
22
==
h
b
x
y
(c)
bh
x ,y
33
==
(d)
hb
x ,y
33
==
Q.6 Two bodies of masses 2 kg and 4 kg are moving with
velocities 2 m/s and 10 m/s respectively along same
direction. Then the velocity of their centre of mass will be
(a) 8.1 m/s (b) 7.3 m/s
(c) 6.4 m/s (d) 5.3 m/s
Q.7 Four particles of masses m, 2m, 3m and 4m are arranged at
the corners of a parallelogram with each side equal to a
and one of the angle between two adjacent sides is 60°.
The parallelogram lies in the x-y plane with mass m at the
origin and 4m on the x-axis. The centre of mass of the
arrangement will be located at
(a)
3
,0.95
2
aa
æö
ç÷
èø
(b)
3
0.95 ,
4
aa
æö
ç÷
èø
(c)
3
,
42
aa æö
ç÷
èø
(d)
3
,
24
aa æö
ç÷
èø
Q.8 Three identical metal balls each of radius r are placed touching
each other on a horizontal surface such that an equilateral
triangle is formed, when centres of three balls are joined.
The centre of the mass of system is located at
(a) Horizontal surface
(b) Centre of one of the balls
(c) Line joining centres of any two balls
(d) Point of intersection of the medians
Q.9 2 bodies of different masses of 2 kg and 4 kg are moving
with velocities 20 m/s and 10 m/s towards each other due
to mutual gravitational attraction. What is the velocity of
their centre of mass?
(a) 5 m/s (b) 6 m/s
(c) 8 m/s (d) Zero
Q.10 Two particles of masses m
1
 and m
2
  initially at rest start
moving towards each other under their mutual force of
attraction. The speed of the centre  of mass at any time t,
when they are at a distance r apart, is
(a) zero (b) 
12
2
1
1
.
mm
Gt
m
r
æö
ç÷
èø
(c)
12
2
2
1
.
mm
Gt
m
r
æö
ç÷
èø
(d) 
12
2
12
1
.
mm
Gt
mm
r
æö
ç÷
+ èø
Q.11 A 'T' shaped object,  dimensions shown in the figure, is
lying on a smooth floor. A force 'F'
r
 is applied at the point
P parallel to AB, such that the object has only the
translational motion without rotation. Find the location of
P with respect to C
(a)
4
3
l
(b) I
(c)
2
3
l                                             
l
B
2l
A
P
C
F
(d)
3
2
l
Q.12 Two spheres of masses 2M and M are initially at rest at a
distance R apart. Due to mutual force of attraction, they
approach each other. When they are at separation R/2, the
acceleration of the centre of mass of spheres would be
(a) 0 m/s
2
(b) g m/s
2
(c) 3 g m/s
2
(d) 12 g m/s
2
Q.13 Masses 8 kg, 2 kg, 4 kg and 2 kg are placed at the corners
A, B, C, D respectively of a square ABCD of diagonal 80
cm. The distance of centre of mass from A will be
(a) 20 cm (b) 30 cm
(c) 40 cm (d) 60 cm
Q.14 If linear density of a rod of length 3m varies as l = 2 + x,
them the position of the centre of gravity of the rod is
(a)
7
m
3
(b)
12
m
7
(c)
10
m
7
(d)
9
m
7
DPP/ P 14
3
Q.15Four bodies of equal mass start moving with same speed
as shown in the figure. In which of the following
combination the centre of mass will remain at origin?
(a) c and d
(b) a and b
(c) a and c
Y
' Y
X
c
b a
d
' X
(d) b and d
Q.16Three identical spheres, each of mass 1 kg are kept as
shown in figure, touching each other, with their centres on
a straight line. If their centres are marked P, Q, R
respectively, the distance of centre of mass of the system
from P is
(a)
3
PQ PR QR ++
(b)
3
PQ PR +
 (c)
3
PQ QR +
x
y
P
Q R
 (d)
3
PR QR +
Q.17 A ladder is leaned against a smooth wall and it is allowed
to slip on a frictionless floor. Which figure represents
trace of motion of its centre of mass
(a) 
Time
(b) 
Time
(c) 
Time
(d) 
Time
Q.18The two particles X and Y, initially at rest, start moving
towards each other under mutual attraction. If at any instant
the velocity of X is V and that of Y is 2V, the velocity of
their centre of mass will be
(a)0 (b) V (c)2V (d) V/2
Q.19 A cricket bat is cut at the location of its centre of mass as
shown in the fig. Then
  
(a) The two pieces will have the same mass
(b) The bottom piece will have larger mass
(c) The handle piece will have larger mass
(d) Mass of handle piece is double the mass of bottom
piece
Q.20 Consider a system of two particles having mass m
1
 and m
2
.
If the particle of mass m
1
 is pushed towards the centre of
mass of particles through a distance d, by what distance
would be particle of mass m
2
  move so as to keep the centre
of mass of particles at the original position?
(a) 
1
12
m
d
mm +
(b)
1
2
m
d
m
(c) d (d)
2
1
m
d
m
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.21Choose the wrong statements about the centre of mass
(CM) of a system of two particles
(1) The CM lies on the line joining the two particles
midway between them
(2) The CM lies on the line joining them at a point whose
distance from each particle is proportional to the
square of the mass of that particle
(3) The CM is on the line joining them at a point whose
distance from each particle is proportional to the mass
of that particle
(4) The CM lies on the line joining them at a point whose
distance from each particle is inversely proportional
to the mass of that particle
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 In  the HCl molecule, the separation between the nuclei of
the two atom is about 1.27 A° (1A° = 10
–10
 m). The
approximate location of the centre of mass from the
hydrogen atom, assuming the chlorine atom to be about
35.5 times massive as hydrogen is
(a) 1 Å (b) 2.5 Å (c) 1.24 Å (d) 1.5 Å
Q.2 A 2 kg body and a 3 kg body are moving along the x-axis. A t
a particular instant the 2 kg bo dy has a velocity of 3 ms
–1
 and the
3 kg body has the velocity of 2ms
–1
. The velocity of the
centre of mass at that instant is
(a) 5 ms
–1
(b) 1 ms
–1
(c)0 (d) None of these
Q.3 The distance between the carbon atom and the oxygen atom
in a carbon monoxide molecule is 1.1 Å. Given, mass of
carbon atom is 12 a.m.u. and mass of oxygen atom is 16
a.m.u., calculate the position of the centre of mass of the
carbon monoxide molecule
(a) 6.3 Å from the carbon atom
(b) 1 Å from the oxygen atom
(c) 0.63 Å from the carbon atom
(d) 0.12 Å from the oxygen atom
Q.4 The velocities of three particles of masses 20g, 30g and
50g are 
ˆ ˆˆ
10 ,10 and10 i jk respectively. The velocity of the
centre of mass of the three particles is
(a)
ˆ ˆˆ
2 3 +5 i jk + (b) 
ˆ ˆˆ
10( +) i jk +
(c)
ˆ ˆˆ
20 30 +5 i jk + (d) 
ˆ ˆˆ
2 30 +50 i jk +
2
DPP/ P 14
Q.5 The centre of mass of a triangle shown in figure has
coordinates
(a)
hb
x= ,y
22
=
(b)
bh
x ,y
22
==
h
b
x
y
(c)
bh
x ,y
33
==
(d)
hb
x ,y
33
==
Q.6 Two bodies of masses 2 kg and 4 kg are moving with
velocities 2 m/s and 10 m/s respectively along same
direction. Then the velocity of their centre of mass will be
(a) 8.1 m/s (b) 7.3 m/s
(c) 6.4 m/s (d) 5.3 m/s
Q.7 Four particles of masses m, 2m, 3m and 4m are arranged at
the corners of a parallelogram with each side equal to a
and one of the angle between two adjacent sides is 60°.
The parallelogram lies in the x-y plane with mass m at the
origin and 4m on the x-axis. The centre of mass of the
arrangement will be located at
(a)
3
,0.95
2
aa
æö
ç÷
èø
(b)
3
0.95 ,
4
aa
æö
ç÷
èø
(c)
3
,
42
aa æö
ç÷
èø
(d)
3
,
24
aa æö
ç÷
èø
Q.8 Three identical metal balls each of radius r are placed touching
each other on a horizontal surface such that an equilateral
triangle is formed, when centres of three balls are joined.
The centre of the mass of system is located at
(a) Horizontal surface
(b) Centre of one of the balls
(c) Line joining centres of any two balls
(d) Point of intersection of the medians
Q.9 2 bodies of different masses of 2 kg and 4 kg are moving
with velocities 20 m/s and 10 m/s towards each other due
to mutual gravitational attraction. What is the velocity of
their centre of mass?
(a) 5 m/s (b) 6 m/s
(c) 8 m/s (d) Zero
Q.10 Two particles of masses m
1
 and m
2
  initially at rest start
moving towards each other under their mutual force of
attraction. The speed of the centre  of mass at any time t,
when they are at a distance r apart, is
(a) zero (b) 
12
2
1
1
.
mm
Gt
m
r
æö
ç÷
èø
(c)
12
2
2
1
.
mm
Gt
m
r
æö
ç÷
èø
(d) 
12
2
12
1
.
mm
Gt
mm
r
æö
ç÷
+ èø
Q.11 A 'T' shaped object,  dimensions shown in the figure, is
lying on a smooth floor. A force 'F'
r
 is applied at the point
P parallel to AB, such that the object has only the
translational motion without rotation. Find the location of
P with respect to C
(a)
4
3
l
(b) I
(c)
2
3
l                                             
l
B
2l
A
P
C
F
(d)
3
2
l
Q.12 Two spheres of masses 2M and M are initially at rest at a
distance R apart. Due to mutual force of attraction, they
approach each other. When they are at separation R/2, the
acceleration of the centre of mass of spheres would be
(a) 0 m/s
2
(b) g m/s
2
(c) 3 g m/s
2
(d) 12 g m/s
2
Q.13 Masses 8 kg, 2 kg, 4 kg and 2 kg are placed at the corners
A, B, C, D respectively of a square ABCD of diagonal 80
cm. The distance of centre of mass from A will be
(a) 20 cm (b) 30 cm
(c) 40 cm (d) 60 cm
Q.14 If linear density of a rod of length 3m varies as l = 2 + x,
them the position of the centre of gravity of the rod is
(a)
7
m
3
(b)
12
m
7
(c)
10
m
7
(d)
9
m
7
DPP/ P 14
3
Q.15Four bodies of equal mass start moving with same speed
as shown in the figure. In which of the following
combination the centre of mass will remain at origin?
(a) c and d
(b) a and b
(c) a and c
Y
' Y
X
c
b a
d
' X
(d) b and d
Q.16Three identical spheres, each of mass 1 kg are kept as
shown in figure, touching each other, with their centres on
a straight line. If their centres are marked P, Q, R
respectively, the distance of centre of mass of the system
from P is
(a)
3
PQ PR QR ++
(b)
3
PQ PR +
 (c)
3
PQ QR +
x
y
P
Q R
 (d)
3
PR QR +
Q.17 A ladder is leaned against a smooth wall and it is allowed
to slip on a frictionless floor. Which figure represents
trace of motion of its centre of mass
(a) 
Time
(b) 
Time
(c) 
Time
(d) 
Time
Q.18The two particles X and Y, initially at rest, start moving
towards each other under mutual attraction. If at any instant
the velocity of X is V and that of Y is 2V, the velocity of
their centre of mass will be
(a)0 (b) V (c)2V (d) V/2
Q.19 A cricket bat is cut at the location of its centre of mass as
shown in the fig. Then
  
(a) The two pieces will have the same mass
(b) The bottom piece will have larger mass
(c) The handle piece will have larger mass
(d) Mass of handle piece is double the mass of bottom
piece
Q.20 Consider a system of two particles having mass m
1
 and m
2
.
If the particle of mass m
1
 is pushed towards the centre of
mass of particles through a distance d, by what distance
would be particle of mass m
2
  move so as to keep the centre
of mass of particles at the original position?
(a) 
1
12
m
d
mm +
(b)
1
2
m
d
m
(c) d (d)
2
1
m
d
m
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.21Choose the wrong statements about the centre of mass
(CM) of a system of two particles
(1) The CM lies on the line joining the two particles
midway between them
(2) The CM lies on the line joining them at a point whose
distance from each particle is proportional to the
square of the mass of that particle
(3) The CM is on the line joining them at a point whose
distance from each particle is proportional to the mass
of that particle
(4) The CM lies on the line joining them at a point whose
distance from each particle is inversely proportional
to the mass of that particle
4
DPP/ P 14
Q.22 Choose the wrong statements about the centre of mass of
a body
(1) It lies always outside the body
(2) It lies always inside the body
(3) It lies always on the surface of the body
(4) It may lie within, outside or on the surface of the body
DIRECTIONS (Q.23-Q.25) : Read the passage given below
and answer the questions that follows :
A system consists of block A and B each of mass m connected
by a light spring as shown in the figure with block B in contact
with a wall. The block A compresses the spring by 3mg/k from
natural length of spring and then released from rest.  Neglect
friction anywhere.
k
3mg/k
B
A
Q.23Acceleration of centre of mass of system comprising A
and B just after A is released is
(a)0 (b)3g/2
(c)3g (d) None of these
Q.24 Velocity of centre of mass of system comprising A and B
when block B just loses contact with the wall
(a) 3
m
g
k
(b)
3
2
gm
k
(c) 2
m
g
k
(d) None of these
Q.25Maximum extension in the spring after system loses
contact with wall
(a)
3
2
mg
k
(b)
3
2
mg
k
(c)
3
2
mg
k
(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 : The centre of mass of a system of n particles
is the weighted average of the position vector of the n
particles making up the system.
Statement-2 : The position of the centre of mass of a
system is independent of coordinate system.
Q.27 Statement-1 : The centre of mass of a proton and an electron,
released from their respective positions remains at rest.
Statement-2 : The centre of mass remains at rest, if no
external force is applied.
Q.28Statement-1 : Position of centre of mass is independent
of the reference frame.
Statement-2 : Centre of mass is same for all bodies.