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HKAL Exercise : Part 1 Mechanics
Chapter 2 Newton’s Laws of Motion
2.1 Newton’s Laws and Momentum
Centre of mass
1.
O
O
O
The above diagram shows a uniform hollow metal cube with a small opening on top. O is the
position of the centre of mass of the hollow cube. What will happen to the position of the
centre of mass of the system as the cube is being slowly filled with oil from the opening ?
A.
B.
C.
D.
It will rise gradually and its final position will be above O.
It will rise gradually at first and then fall to its original position.
It will fall gradually at first and then rise to its original position.
It will remain unchanged throughout the process.
Momentum
2. Two objects of masses 9 m and m move
towards each other along a straight line
with kinetic energies E and 9 E
respectively. The total linear momentum
of both masses taken together is
A. 0.
B.
C.
D.
3 2mE .
6 2mE .
9 2mE .
3.
m
v
v


m
A gas atom of mass m moving with a
uniform speed v makes an elastic collision
with the wall of the container as shown in
the diagram. What is the magnitude of the
change in the momentum of the gas
atom ?
A. 2mv
B. mv sinθ
C. 2mv sinθ
D. 2mv cosθ
Equilibrium
4. A smooth block of mass 6 kg slides down a wedge. The wedge, of mass 20 kg, is placed on a
horizontal table, and its inclined plane makes an angle of 30∘with the horizontal. If the wedge
remains stationary all the time, the normal reaction of the table acting on the wedge is
A. 45 N.
B. 200 N.
C. 245 N.
D. 290 N.
HKAL Extra Exercise_Chapter 2 Newton’s Laws of Motion
1/14
5.
acceleration
A. 31 N.

A bob of mass m is suspended from a
fixed support by a light string. A force F is
applied to the bob (F is not shown in the
figure) so that the string makes an angle
θ with the vertical. What is the
minimum value of F required to keep the
bob in static equilibrium as shown ?
A. mgsinθcosθ
B.
C.
D.
mgcosθ
mgsinθ
mgsin2θ
46 N.
56 N.
69 N.
7.
P
rod
motor
propeller
The above figure shows a propeller-motor
system connected by a light, rigid rod to a
fixed point P on the ceiling. The system
remains stationary when the motor is on.
Which of the following diagrams correctly
represents the force acting on the
propeller-motor system ?
A.
B.
6.
F
20 cm
B.
C.
D.
horizontal
surface
A block of mass 10 kg is placed on the
inclined surface of the wedge shown
above. All contact surfaces are assumed to
be smooth. What is the magnitude of the
horizontal force F exerted on the wedge so
that it remains stationary while the block
is sliding down the inclined surface with
C.
D.
Addition of forces
8.
F1
F2
The resultant of two forces F1 and F2 acting at a point can have a minimum value of 1 N and a
maximum value of 9 N. When the two forces act at right angles to each other, the magnitude of
their resultant is
A.
C.
4N
8N
B.
D.
41 N
90 N
HKAL Extra Exercise_Chapter 2 Newton’s Laws of Motion
2/14
Newton’s Second Law of Motion
9.
Which of the following pairs of quantities
of a moving object must be in the same
direction ?
(1) displacement and velocity
(2) momentum and velocity
(3) force and change in momentum
A. (1) only
B. (3) only
C. (2) and (3) only
D. (1), (2) and (3)
12.
F
proportional to t .
proportional to 1/ t .
C
Three blocks A, B and C of masses m, 4m
and 4m respectively are placed on a
smooth horizontal ground as shown in the
figure above. A constant horizontal force
is applied to block A so that the three
blocks move with the same acceleration
towards the right. What is the resultant
force acting on block B ?
A. F/9
B. 4F/9
C. 5F/9
D. F/5
10. A solid of mass starts from rest and travels
for a given time t under the action of a
given force. The speed which it acquires is
A. proportional to t.
B. proportional to 1/t.
C.
D.
A B
13.
11.
axle
P
A
B
Q
Two blocks A and B of mass ratio 2 : 5 are
placed on a horizontal frictionless surface
as shown above. P and Q are horizontal
forces acting on A and B respectively
(with P > Q) so that the blocks move to
the right with constant acceleration. Find
the force acting on B by A.
A.
5P  2Q
7
B.
2 P  5Q
7
C.
PQ
7
D.
PQ
7
HKAL Extra Exercise_Chapter 2 Newton’s Laws of Motion
3 kg
5 kg
An object of mass 5 kg is tied to another
object of mass 3 kg with a string passing
over a fixed smooth pulley. The weight of
the pulley is negligible. When the objects
move under the action of gravity, the
vertical upward force acting on the axle of
the pulley is
A. zero.
B. 20 N.
C. 80 N.
D. 84 N.
3/14
14.
17. A force F is applied to an initially
stationary particle from time t = 0. F
7 kg
30O
2 kg
An object of mass 2 kg is placed on a
smooth plane inclined at 30 ∘ to the
horizontal. It is connected by a light string
passing over a frictionless pulley to
another object of mass 7 kg, as shown
above. Given that g = 10 m/s2, when the
system is released, the tension in the string
will be
varies sinusoidally with time t as shown in
the following graph :
F
0
Which of the following graphs best
represents the variation of the subsequent
velocity v of the particle with t ?
A. 23 N.
B. 28 N.
C. 31 N.
D. 70 N.
15. A spacecraft of mass 5.0 × 104 kg was
A.
travelling on its way to the moon with the
rocket motors shut down. At the instant
when it was travelling at 1700 m/s, the
rocket motors were turned on for 6
seconds to make a course correction. If the
rocket gave a thrust of 3.0 × 105 N at
0
right angles to the direction of travel,
through what angle would the flight path
of the spacecraft be turned ?
A. 2.1 × 10-3 rad
B. 3.5 × 10-3 rad
C. 2.1 × 10-2 rad
D. 3.5 × 10-2 rad
16. A student holds one end of a string to
which a block of mass 4 kg is tied at the
other end. He raises the block with an
acceleration by pulling the string in an
upward direction. If the maximum tension
that the string can withstand is 100 N, find
the maximum acceleration of the block
before the string breaks.
A. 12.5 m s-2
B. 15.0 m s-2
C. 20.0 m s-2
D. 25.0 m s-2
HKAL Extra Exercise_Chapter 2 Newton’s Laws of Motion
t
v
t
B.
v
0
t
C.
v
0
t
D.
v
0
t
4/14
18. Before the start of a race, the momentum of each competitor is less than his momentum during
the race. Which of the following statements is/are correct ?
(1) A force acts on each competitor to increase his momentum as he starts to race.
(2) The law of conservation of momentum applies only to collisions between two objects.
(3) This situation obeys Newton’s law of conservation of momentum.
A. (1) only
B. (2) only
C. (1) and (3) only
D. (1), (2) and (3)
Feeling of One’s Weight
19. A lift of mass M carries a man of mass m.
(5)moving downwards and decelerating at g/10.
When the lift is being hauled upward by a
A. (1) only
rope, the lift rises with an acceleration a.
The tension of the rope is
A. m (g - a).
B. (m + M) (g + a).
C. m (g + a) - Ma.
D. m (g + a) + Ma.
20. A man weights an object with a spring
balance in a lift. Before the lift moves the
scale reads 30 N. The lift goes up and then
stops. The reading on the scale is
A.
B.
C.
D.
more than 30 N when the lift starts,
and remains steady until it comes to
rest.
less than 30 N when the lift starts,
and remains steady until it comes to
rest.
more than 30 N as the lift starts, and
less than 30 N as it comes to rest.
less than 30 N as the lift starts, and
more than 30 N as it comes to rest.
21. A man in a lift measures his weight with a
compression balance and discovers that
his weight is increased by 10%. The lift is
probably
(1)moving downwards with uniform velocity.
(2)moving upwards and accelerating at g/10.
(3)moving upwards and decelerating at g/10.
(4)moving downwards and accelerating at g/10.
B.
C.
D.
22. A man of weight W stands on a
compression balance placed inside a lift.
The velocity-time graph of the lift is
shown below (The upward direction is
taken to be positive) :
velocity
0
t1
time
t2
Which of the following graphs best shows
the variation of the reading on the balance,
R, with time, t ?
A.
B.
R
R
W
0
W
t 1 t2
t
C.
0
t1 t2
t
D.
R
R
W
0
HKAL Extra Exercise_Chapter 2 Newton’s Laws of Motion
(1) and (3) only
(1) and (4) only
(2) and (5) only
W
t1 t2
t
0
t 1 t2
t
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2.2 Momentum and Impulse
Impulse
23. Steel ball bearings, each of mass m, are
fired at the rate of n ball bearings per
second towards a fixed vertical steel block
with a horizontal speed v. Their horizontal
speed become zero after colliding with the
wall. The average force exerted on the
block is
A. zero.
B.
C.
D.
26. A softball of mass 0.5 kg flies horizontally
with a speed of 0 m s-1 towards a player.
After being hit by the bat, it flies away at
50 m s-1 perpendicular to its original
direction. Find the magnitude of the
impulse acting on the softball.
A. 10 kg m s-1
B. 29 kg m s-1
mnv.
2mnv.
2mgnv.
C.
D.
40 kg m s-1
58 kg m s-1
27.
24. The work done on a thermally isolated
object is equal to its change in
A. velocity.
B. momentum.
C. kinetic energy.
D. mechanical energy.
25.
final
momentum
North
60O
initial
momentum
The initial momentum of an object is 3
N s due west and its final momentum is 2
N s in the direction N 60∘W. If this
change takes place in 2 s, the average
force acting on the object during the
change is
A. 0.5 N due north.
B. 0.5 N due south.
C. 1 N due south.
D. 1 N due north.
HKAL Extra Exercise_Chapter 2 Newton’s Laws of Motion
F/N
4
0
5
t/s
The graph shows the time variation of the
net force, F, acting on an object of mass 1
kg. The object is initially at rest and its
subsequent motion is along a straight line.
Which of the following statements is/are
correct ?
(1) The object is accelerating in the first
5 seconds.
(2) The final speed of the object is zero.
(3) The maximum speed of the object is
less than 10 m s-1.
A.
B.
C.
D.
(1) only
(3) only
(1) and (2) only
(1), (2) and (3)
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Principle of Conservation of Momentum
28. A box moves at a uniform velocity of 8
m/s on a frictionless horizontal surface.
Sand falls into the box with negligible
speed at a rate of 45 kg per minute. What
horizontal force is required to keep the
box moving uniformly at 8 m/s ?
A. 0 N
B. 6 N
C. 45 N
D. 360 N
30. A nucleus originally at rest splits into two
fragments of unequal mass. The two
fragments have the same
(1) kinetic energy.
(2) speed.
(3) momentum.
A. (1) only
B. (3) only
C. (1) and (2) only
D. (2) and (3) only
29.
31. A spaceship burns fuel and moves with
constant acceleration in a straight line.
Which of the graphs below best represents
the variation of its upthrust F with time t?
A.
B
The above figure shows an open wagon
moving with negligible resistance in
vertically falling rain. An appreciable
amount of rain falls into the wagon and
accumulates there. What are the effects of
A.
B.
C.
D.
the accumulating rain on the speed,
momentum and kinetic energy of the
wagon ? (Ignore the effects of the rain
drops hitting the front of the wagon.)
kinetic
speed
momentum energy
unchanged
unchanged
unchanged
unchanged
increased
increased
decreased
unchanged
decreased
decreased
unchanged
unchanged
F
0
F
t
C
t
D
F
0
0
F
t
0
t
Three types of collision
32. A sphere X of mass m, travelling with speed u, makes a head-on collision with a similar sphere
Y which is at rest. After the collision the velocities of X and Y are v1 and v2 respectively. Which
one of the following is a possible pair of values for v1 and v2?
v1
v2
v1
v2
A.
C.
u/ 2
2u/3
u/ 2
u/3
B.
D.
u/2
u/3
HKAL Extra Exercise_Chapter 2 Newton’s Laws of Motion
3 u/2
2u/3
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33.
P
X
Q
Y
R
Z
P, Q and R are three identical spheres moving with the same speed along a smooth horizontal
track. They undergo head-on elastic collisions with spheres X, Y and Z respectively which are
initially at rest. After collision, P continues to move in its original direction, Q becomes
stationary while R reverses its motion. After collision, which sphere (X, Y or Z) has the greatest
magnitude of
(1) kinetic energy
(2) momentum ?
(1)
(2)
A. X
Z
B. Y
Z
C. Z
X
D. Z
Y
Elastic Collision
34. In a partially elastic collision between two
bodies, and in the absence of external
forces,
A. kinetic energy and momentum
are both conserved.
B. kinetic energy is conserved but
C.
D.
momentum is not conserved.
kinetic energy is not conserved
but momentum is conserved.
neither kinetic energy nor
momentum is conserved.
A.
B.
C.
D.
(1) only
(1) and (2) only
(2) and (3) only
(1), (2) and (3)
36.
X
m
u
Y
m
Z
5m
C
35. A sphere X moving with velocity u on a
smooth horizontal plane makes a head-on
collision with another sphere Y of the
same mass which is initially at rest. If the
X, Y and Z are three spheres of the same
size but with masses m, m and 5m
respectively, lying on a smooth horizontal
track with Y and Z in contact as shown. X
is moving to the right with velocity u and
makes a head-on collision with Y. If all
collisions are perfectly elastic, which of
collision is inelastic, which of
following statements is/are correct ?
(1) Linear momentum is conserved in
collision.
(2) X and Y stick together and move off
the same velocity after the collision.
(3) Kinetic energy is conserved in
collision.
the following gives the possible velocities
of the three spheres after all collisions ?
(Take to the right as positive.)
X
Y
Z
A. -2u/3
0
u/3
B. 0
u/6
u/6
C. 0
-2u/3
u/3
D. u/7
u/7
u/7
the
this
with
this
HKAL Extra Exercise_Chapter 2 Newton’s Laws of Motion
8/14
Collisions in 2-dimension
37. An alpha particle colludes with a stationary helium nucleus ( 24 He ) in a cloud chamber. Which
of the following diagrams represents the most probable set of tracks?
A.
B.


4
2He

C.
4
2He

D.


4
2He


4
2He
2.3 Friction
Static Friction
38.
39.
A
B
F
Two wooden blocks A and B are
connected by a string which passes over a
smooth, fixed pulley as shown. The
maximum friction between any two
surfaces is 5 N. If a horizontal force F is
applied to block B, find its minimum value
for moving B.
A. 5 N
B.
C.
D.
15 N
20 N
25 N
HKAL Extra Exercise_Chapter 2 Newton’s Laws of Motion
F
A
B
Two blocks A and B are placed on a
horizontal table surface as shown. A
horizontal force F is applied to A but the
system remains stationary. Which of the
following statements is/are correct ?
(1) The frictional force acting on B by the
table surface is equal to F.
(2) The system would remain stationary if F is
applied to B instead.
(3) The frictional force acting on B by A is
towards the left.
A. (1) only
B. (3) only
C. (1) and (2) only
D. (1), (2) and (3)
9/14
40. A block rests on a rough inclined plane. Which of the following diagrams correctly shows the
lines of application of all the forces acting on the block ? (The dot  represents the centre of
mass of the block.)
A.
B.
C.
D.
Kinetic Friction
41.
43.
B
P
M
A horizontal force P is applied to a
wooden block at rest on a rough horizontal
table. P is increased uniformly from zero.
Which of the following graphs best
describes the variation of the frictional
force acting on the block with P?
A.
B.
F
0
F
P
0
C.
D.
F
F
0
P
0
P
P
15 m
A
40O
40O
C
A small block M of mass 1 kg is
transported across a small hill along the
road ABC by an applied force F which is
always parallel to the road. The speed of
M is kept constant throughout the journal
and the kinetic friction between the block
and the road is 1.40 N. The total work
done by F in transporting M from A to C is
A. zero.
B. 65 J.
C. 300 J.
D. 365 J.
44. When given a slight push, a toy car moves
freely with constant velocity down a plane
inclined at 30∘to the horizontal. If the
mass of the car is 2 kg, find the force
42. An object of mass m slides with constant
acceleration a down a plane making an
angle θ with the horizontal. The
frictional force acting on the object is
A. mg - ma sinθ
B. mg sinθ- ma
C. (mg – ma) sinθ
D. (ma - mg)sinθ
HKAL Extra Exercise_Chapter 2 Newton’s Laws of Motion
parallel to the inclined plane for pulling
the car up the plane with constant velocity.
A. 10 N
B. 20 N
C. 25 N
D. 30 N
10/14
45. A trolley of mass 2.0 kg moves with a certain acceleration down a runway which is inclined to
the horizontal at 25∘. If the angle of inclination is increased to 30∘, the acceleration of the
trolley would be doubled. Find the average frictional force, assuming the same in both cases,
acting on the trolley.
A. 6.21 N
B. 6.90 N
C. 7.59 N
D. 8.28 N
Pulley
46. A builder using a pulley system to lift a bucket of cement of weight 200 N exerts a steady force
F and pulls 40 m of rope through the system in order to raise the bucket 15 m. The friction in
the system is small but NOT negligible. The value of the force F is most probably
A.
B.
C.
D.
exactly equal to 75 N.
between 75 N and 150 N.
between 200 N and 533 N.
more than 533 N.
2.4 Spring and Force Constant
47.
48.
B
A
P
Y
Q
Two bodies P and Q are connected by a
light string A. The weights of P and Q are
4 N and 12 N respectively. P is connected
to the roof by another light string B. If
string B is cut and the bodies allowed to
fall, the net force acting on Q during free
fall is
A.
B.
C.
D.
4 N.
8 N.
12 N.
16 N.
HKAL Extra Exercise_Chapter 2 Newton’s Laws of Motion
X
Two identical blocks X and Y are
connected by a light spring and the system
is suspended from a fixed support by a
light cord as shown. The system is in static
equilibrium. If the cord is suddenly cut,
what is the magnitude of the acceleration
of each block at that instant ?
Acceleration Acceleration
of X
of Y
A.
zero
g
B.
zero
2g
C.
g
g
D.
g
2g
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49.
51
spring A
2N
A
spring B
6N
B
Two objects of weights 2 N and 6 N are
suspended from a fixed point by two
identical light springs A and B as shown in
the diagram. The force constants of the
springs are both 1 N/cm. What are the
extensions of springs A and B ?
A.
B.
C.
D.
Extension
of spring A
2 cm
8 cm
2 cm
8 cm
Extension
of spring B
4 cm
4 cm
6 cm
6 cm
50
The figure shows two blocks A and B, of
masses m and 4 m respectively, connected
by two light springs to a fixed support.
Each spring has a force constant k. What is
the total extension of the system when it is
at static equilibrium ?
A. mg/k
B. 5mg/(4k)
C. 5mg/k
D. 9mg/k
D
52.
h
2.0 kg
1.0 kg
Two identical light springs are connected
with two masses of 2.0 kg and 1.0 kg as
shown. Which of the following statements
is/are correct ?
(1) The tension in the upper spring is triple
that in the lower spring.
(2) The force acting on the ceiling by the
A light spring is fixed to the bottom of a
vertical tube. A ball is released from rest at
a height h above the upper end of the
spring as shown. After rebounding several
times the ball eventually comes to rest and
stays on top of the spring. Assume all
contact surfaces are smooth and the spring
whole system is 10 N.
(3) The tension in the upper spring will
remain unchanged if the two masses are
exchanged in position.
A. (1) only
B. (1) and (3) only
C. (2) and (3) only
D. (1), (2) and (3)
obeys Hooke’s law throughout. Which of
the following statements is/are correct ?
(1) The compression of the spring is
independent of the height h.
(2) The gravitational potential energy lost by
the ball is equal to the strain energy stored
in the spring.
(3) The compression of the spring is
HKAL Extra Exercise_Chapter 2 Newton’s Laws of Motion
12/14
independent of the mass of the ball.
A. (1) only
B.
C.
D.
54.
(1) and (2) only
(2) and (3) only
(1), (2) and (3)
A trolley travels with constant velocity to
the right on horizontal ground and collides
with a light helical spring attached to a
wall fixed to the ground (earth) as shown.
At the instant that the trolley comes
momentarily to rest during collision, what
has happened to the initial momentum of
53.
A
B
C
the trolley ?
A. It has been dissipated as sound
and heat.
B. It has been destroyed by the
friction due to the ground.
C. It has been lost because the
collision was not perfectly
elastic.
D. It has been transferred to the
earth.
A block of mass m falls from rest at A onto
a vertical light spring of force constant k
firmly fixed to the ground. When the block
reaches B, it starts to compress the spring
until it reaches the lowest position C as
shown. Neglecting air resistance and
considering the motion of the block from
A to C, which of the following statements
is/are correct ?
(1) The resultant force acting on the
block is pointing upward when it is at
C.
(2) The maximum compression of the
mg
spring is greater than
.
k
(3) The kinetic energy of the block is at a
maximum when it is at B.
A. (1) only
B.
C.
D.
(3) only
(1) and (2) only
(2) and (3) only
HKAL Extra Exercise_Chapter 2 Newton’s Laws of Motion
55
P
S
X
Y
30O
30O
In the figure above, X and Y are blocks of
mass 1 kg and 4 kg respectively. S is a
spring balance of negligible mass and P is
a smooth pulley fixed at the top of two
smooth inclined planes. What is the
reading of S when X is held stationary ?
A. 15 N
B. 20 N
C. 35 N
D. 40 N
13/14
56
A
B
F
Two objects A and B of equal mass m are connected by two identical light springs and are
placed on a horizontal smooth surface. A horizontal force F is applied to B so that the system is
in equilibrium. If the applied force F is suddenly removed, what are the magnitudes of the
acceleration of each object at the instant when force F is removed ?
Acceleration of A Acceleration of B
A.
zero
zero
B.
zero
F
m
C.
F
m
zero
D.
F
m
F
m
2.5 Work and Energy
Work
57. Two objects A and B of masses m and 2m
respectively are initially at rest on a
smooth, horizontal surface. If each of
them is acted upon by the same force for
the same distance, the ratio of the gain in
kinetic energy of A to that of B is
A. 1 : 1.
B. 1 : 2.
C. 1 : 4.
D. 2 : 1.
Kinetic energy
58.
E/J
1
0
1
v/ms
The above graph shows the variation of
kinetic energy E with the velocity v of a
moving mass m. What is the momentum of
the mass when it is moving at a speed of 2
m s-1 ?
A. 1 N s
B. 2 N s
C.
D.
4Ns
8Ns
KEY :
1 – 10 : CACCC, BABCA, 11 – 20 : ABCAC, BBCBC, 21 – 30 : DBBDA, BABCB,
31 – 40 : ADBCB, ABBCA, 41 – 50 : BBBAB, BCBDB, 51 – 56 : DACDB, BAC.
HKAL Extra Exercise_Chapter 2 Newton’s Laws of Motion
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