Laws of Motion Notes and MCQs

Notes 27 Pages

Joint Entrance Examination (Main)

Physics

Contributed by

Yash Kuruvilla

51
Unit - 3
Laws of Motion
Page 1
52
SUMMARY
Important Points
 The law of inertia given by Galileo was represented by Newton as the first law of motion :" If no external
force acts on a body, the body at rest remains at rest and a body in motion continues to move with the
same velocity."
This law gives us definition of force.
 The momentum of a body

 vmp is a vector quantity.It gives more information than the velocity.It's
unit is
1
kgms

or Ns and dimensional formula M
1
L
1
T
-
1
.
 Newton's second law of motion : The time-rate of change in momentum of a body is equal to the
resultant external force applied on the body and is in the direction of the exterrnal force.

F
=
dP
dt
ma


is the vector relationship
The SI unit of force is newton (=N) . 1 N = 1 kg ms
–
2

. This law gives the value of force.It is consistent
with the first law.(

F
=0 indicates that
a

=0). In this equation the acceleration of the body
a

is that
which it has when the force is acting on it.(Not of the Past!) .

F
is only the resultant external force.
 The impulse of force is the product of force and the time for which it acts. when a large force acts for
a very small time, it is difficult to measure

F
and t but the change in momentum can be measured,
which is equal to the impulse of force (

F

t
)
 Newton's third law of motion: " To every action there is always an equal and opposite reaction."
Forces always act in pairs, and,

F
AB
= –

F
BA
. The action and the reaction act simultaneously.They act on
different bodies,hence they cannot be cancelled by adding. But the resultant of the forces between
different parts of the same body becomes zero.
 The law of conservation of momentum is obtained from Newton's second law and the third law.It is
written as-"The total momentum of an isolated system remains constant."
 The concurrent forces are those forces of which the lines of action pass through the same point. For
equilibrium of the body, under the effect of such forces,


F
must be = 0 Moreover, the sum of the
corresponding components also should be zero. (

F
x
= 0,

F
y
=o, F
z
= 0)
- Friction is produced due to the contact force between the surfaces in contact.It opposes the impending or
the real relative motion.
Static frictional force
f
s


f
s

(max)
=

s
N and the kinetic friction is f
k
=

k
N
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53
S
µ  coefficient of static friction
k
µ 

coefficient of kinetic friction and
k s
  
* The reference frame , in which Newton's first law of motion is obeyed is called the inertial frame of
reference and the one in which it is not obeyed is called non-inertial frame of reference. The frame of
reference with constant velocity is an inertial frame of reference and one which has acceleration is non-
inertial frame of reference.
* On a body performing uniform circular motion a force equal to mv
2

/ r acts towards the centre of the
circular path. This is called the centripetal force.
The maximum safe speed on level curved road is v
max
= rgµ
s
The maximum safe speed on a banked curved road is v
max
=










tanθµ1
tanθµ
rg
s
s
* Motion of a body on a friction less inclined plane:
As shown in figure body of mass m is placed on a smooth inclined plane making an angle
θ
with the
horizontal.
Here,
 
Ncosmg1 
†ÃÜå
 
masinmg2 

acceleration of body
θ
= gsin
θ
.
* Motion of a body on a Rough inclined plane:
(1) Body moving down : If body moving down
with acceleration a then,
mg sin
θ
– maNµ
s
 and N = mg cos
θ
 
macosθmgµsinθmg
s


a


cosθµsinθg
s

(2) Body moves up : If body is moving upwards with acceleration a then


s
g sin θ μ cos θ .a  
 Pseudo Force : In non-inertial frame of reference due to acceleration one more additional force acting on
a body in the opposite direction of acceleration of frame of reference is called pseudo force (F
P
) .
 when a man of weight m climbs on the rope with acceleration a then tension in the rope is T = m(g + a).
 When man sliding down with acceleration a then tension in the rope is T = m(g – a).
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54
* When masses in contact:
In figure masses
m
1
,
m
2
and
m
3

are placed in contact on a surface.
acceleration
1 2 3
F
a
m m m

 
Force on
m
1

:
F
1

= F
Force on
m
2

: F
2

= (m
2

+ m
3
)


2 3
1 2 3
m m F
a
m m m


 
Force on m
3

:
 
3
3 3
1 2 3
m F
F m a
m m m
 
 
* Masses connected by strings:
Consider two masses
1
m
and
2
m
placed on a frictionless horizontal surface connected by a light
inextensibule string.
If
1
m
is pulled by a force F then a tension T is developed,
in the string.
For
1
m
:
For
1 2 2
F –T = m a , m : T = m a

Tension in string
2
1 2
,
m F
T
m m


acceleration
1 2
.
F
a
m m


a
2
m
1
m
T T
F
F
a
1
m
2
m
3
m
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MCQ
For the answer of the following questions choose the correct alternative from among the given ones.
1. The velocity of a body of mass 20 kg decreases from 20 ms
–
1

to 5 ms
–
1

in a distance of 100 m. Force
on the body is
(A) -27.5 N (B) -47.5 N (C) -37.5 N (D) -67.5 N
2. A ball of mass 0.2 kg is thrown vertically upwards by applying a force by hand. If the hand moves
0.2 m while applying the force and the ball goes upto 2 m height further, find the magnitude of the
force. (Consider g = 10 ms
–
2
)
(A) 16 N (B) 20 N (C) 22 N (D) 4 N
3. Formula for true force is
(A)
F ma

(C)
 
d mv
F
dt

(B)

dv
F m
dt

(D)
2
2
d x
F = m
dt
4. A particle moves in the X–Y plane under the influence of a force such that its linear momentum is
^ ^
P (t) A[ i cos (kt) j sin(kt)]

 
where A and k are constants. The angle between the force and
momentum is
(A) 0
0
`
(B) 30
0
(C) 45
0
(D) 90
0
5. Force of 5 N acts on a body of weight 9.8 N. what is the acceleration produced in ms
-
2
(A)49.00 (B) 5.00 (C) 1.46 (D) 0.51
6. A lift is going up. The total mass of the lift and the passenger is 1000 kg The variation in the speed of
the lift is as given in the graph. The tension in the rope pulling the lift at t= 10.5 sec will be
(A) 8000 N
(B) Zero
(C) 12000 N
(D) 17400 N
7. Same force acts on two bodies of different masses 2 kg and 4 kg initially at rest. The ratio of times
required to acquire same final velocity is
(A) 2:1 (B) 1:2 (C) 1:1 (D) 4:16
8. Which of the following quantities measured from different inertial reference frames are same
(A) Force (B) Velocity (C) Displacement (D) Kinetic Energy
2 10 12
3.6
1
t (sec)
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9. 10,000 small balls, each weighing 1 g strike one square cm of area per second with a velocity
100 ms
–1

in a normal direction and rebound with the same velocity. The value of pressure on the surface
will be
(A)
23
Nm102


(B)
25
Nm102


(C)
27
Nm10

(D)
27
Nm102


10. When the speed of a moving body is doubled
(A) Its acceleration is doubled
(B) Its momentum is doubled
(C) Its kinetic energy is doubled
(D) Its potential energy is doubled
11. A particle moves in the XY Plane under the action of a force F such that the components of its linear
momentum P at any time t are Px = 2 cost, Py = 2 sint. The angle between F and P at time t is
(A) 90
0
(B) 0
0
(C) 180
0
(D) 30
0
12. A player caught a cricket ball of mass 150 g moving at the rate of 20 ms
-
1

. If the catching process be
completed in 0.1 s the force of the blow exerted by the ball on the hands of player is
(A) 0.3 N (B) 30 N C) 300 N (D) 3000 N
13. A body of mass 5 kg starts from the origin with an initial velocity
^ ^
-1
u=30 i +40 j ms

. If a constant
Force
–
^ ^
F= i +5 j N
 
 
 

acts on the body, the time in which the y-component of the velocity becomes
zero is
(A) 5 s (B) 20 s (C) 40 s (D) 80 s
Third law of motion
14. Swimming is possible on account of
(A) First law of motion (B) second law of motion
(C) Third law of motion (D) Newton's law of gravitation
15. A cold soft drink is kept on the balance.When the cap is open, then the weight
(A) Increases (B) Decreases (C) First increase then decreases (D) Remains same
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Conservation of linear momentum and impulse
16. A wagon weighing 1000 kg is moving with a velocity 50 km h
-
1

on smooth horizontal rails. A mass
of 250 kg is dropped into it. The velocity with which it moves now is
(A)
1
hkm5.2

(B)
1
hkm20

(C)
1
hkm40

(D)
1
hkm50

17. The Figure shows the Position-time (x-t) graph of one dimensional motion of a body of mass 0.4 kg .
The magnitude of each impluse is
(A) 0.2 Ns (B) 0.4 Ns
(C) 0.8 Ns (D) 1.6 Ns
Equllibrium of Forces
18. Three Forces F
1
, F
2

and F
3
together keep a body in equilibrium. If F
1

= 3 N along the positive X- axis,
F
2

= 4N along the positive Y-axis ,then the third force F
3

is
(A) 5 N -making an angle
θ
= tan
–
1



4
3
with negative y-axis
(B) 5 N - making an angle
θ
= tan
–
1



3
4
with negative y-axis
(C) 7 N - making an angle
θ
= tan
–
1



4
3
with negative y-axis
(D) 7 N - making an angle
θ
= tan
–
1



3
4
with negative y-axis
19. A solid sphere of mass 2 kg is resting inside a cube as shown in the figure. The cube is moving with
a velocity
–
^ ^
1
v = 5t i+ 2t j ms
 
 
 

Here t is the time in second. All surfaces are smooth. The sphere
is at rest with respect to the cube. what is the total force exerted by the sphere on the cube
(g = 10 ms
–
2
)
(A)
N29
(B) 29 N
(C) 26 N (D)
N89
y
0
x
A B
D C
x (m)
0 2 4 6 8 10 12 14 16
t (s)
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58
20. A particle of mass 2 kg is initially at rest. A force acts on it whose magnitude changes with time. The
force time graph is shown below.
The velocity of the particle after 10s is
(A) 10 ms
-
1
(B) 20 ms
-
1
(C) 75 ms
-
1
(D) 50 ms
-
1
21. A block of mass 4 kg is placed on a rough horizontal plane. A time dependent force F = Kt
2

acts on
a block , where k = 2
2
s
N
, co-efficient of friction
0.8µ 
.Force of friction between the block and the
plane at t = 2 S is.....
(A) 32 N (B) 4 N (C) 2 N (D) 8 N
22. A 7 kg object is subjected to two forces (in newton)
^ ^
1
F =20i+30 j

and
^ ^
2
F = 8i-5 j

The magnitude of
resulting acceleration in ms
–
2

will be
(A) 5 (B) 4 (C) 3 (D) 2
23. A car travelling at a speed of 30 km/h is brought to a halt in 8 metres by applying brakes. If the same
car is travelling at 60 km/h it can be brought to a halt with the same breaking power in
(A) 8 m (B) 16 m (C) 24 m (D) 32 m
24. A given object takes n times more time to slide down 45
0
rough inclined plane as it takes to slide down
a perfactly smooth 45
0
incline. The coefficient of kinetic friction between the object and the incline is
(A)
2
1
2 n
(B)
2
1
1
n

(C)
2
1
1
n

(D)
2
1
1 - n
25. Two bodies of equal masses revolve in circular orbits of radii R
1
and R
2
with the same period Their
centripetal forces are in the ratio.
(A)
2
1
2
R
R








(B)
2
1
R
R
(C)
2
2
1
R
R






(D)
1 2
R R
26. Two masses M and
2
M
are joined together by means of light inextensible string passed over a
frictionless pulley as shown in fig. When the bigger mass is released, the small one will ascend with an
acceleration
(A)
3
g
(B)
3
2
g
(C) g (D)
2
g
0
10
20
F (N)
t (s)
2
M
M
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59
27. A 0.5 kg ball moving with a speed of 12 ms
-
1

strikes a hard wall at an angle of 30
0
with the wall.
It is reflected with the same speed and at the same angle. If the ball is in contact with the wall for
0.025 S the average force acting on the wall is
(A) 96 N (B) 48 N (C) 24 N (D) 12 N
28 A shell of mass 200g is ejected from a gun of mass 4 kg by an explosion that generates 1.05 KJ of
energy. The initial velocity of the shell is
(A) 100 ms
-
1
(B) 80 ms
-
1
(C) 40 ms
-
1
(D) 120 ms
-
1
29. A gramophone record is revolving with an anguler velocity  A coin is placed at a distance r from the
centre of the record. The coefficient of static friction is
µ
. The coin will revolve with the record if
(A) r =
µ
g
2
(B)
2
r
µg


(C)
2
µg
r


(D)
2
µg
r


30. A stone of mass 2 k g is tied to a string of length 0.5 m It the breaking tension of the string is 900N,
then the maximum angular velocity the stone can have in uniform circular motion is
(A) 30 rad/s (B) 20 rad/s (C) 10 rad/s (D) 25 rad/s
31. A body of mass 6 kg is hanging from another body of mass 10 kg as shown in fig. This conbination is
being pulled up by a string with an acceleration of 2 ms
–
2
. the tension T
1

is (g = 10 ms
–
2

)
(A) 240 N
(B) 150 N
(C) 220 N
(D) 192 N
32. A sparrow flying in air sits on a stretched telegraph wire. If the weight of the sparrow is W ,which of the
following is true about the tension T produced in the wire?
(A) T = W (B) T < W (C) T = 0 (D) T >W
33. Fig. shows the displacement of a particle going along X-axis as a function of time. The force acting on
the particle is zero in the region
(A) AB
(B) BC
(C) CD
(D) None of these
T
1
10 kg
6 kg
a
T
2
X
A
Displacement
B C
D
Time
Y
Page 9
60
34. A Force (F) varies with time (t) as shown in fig. Average force over a complete cycle is-
(A) Zero (B)
2
F
0
(C)

0
F
(D)
0
F2
35. A body of mass 0.05 kg is falling with acceleration 9.4 ms
–
2

. The force exerted by air opposite to
motion is N (g=9.8 ms
–
2
)
(A) 0.02 (B) 0.20 (C) 0.030 (D) Zero
36. The average force necessary to stop a hammer with 25 NS momentun in 0.04 sec is ___________N
(A) 625 (B) 125 (C) 50 (D) 25
37. Newton's third law of motion leads to the law of consrevation of
(A) Angular momentum (B) Energy (C) mass (D) momentum
38. A ball falls on surface from 10 m height and rebounds to 2.5 m. If duration of contact with floor is
0.01 sec. then average aceleration during contact is _______________ms
-
2
(A) 2100 (B) 1400 (C) 700 (D) 400
39. A vehicle of 100 kg is moving with a velocity of 5
s
m
. To stop it in
10
1
sec, the required force
in opposite direction is _______________N
(A) 50 (B) 500 (C) 5000 (D) 1000
40. The linear momentum P of a particle varies with the time as follows.
2
btaP 
Where a and b are
constants. The net force acting on the particle is _____________
(A) Proportional to t (B) Proportional to t
2
(C) Zero (D) constant
41. A vessel containing water is given a constant acceleration a towards the right, along a straight horizontal
path. which of the following diagram represents the surface of the liquid ?
(A) (B) (C) (D)
42. A body of 2 kg has an initial speed 5 m/s. A force act on it for some time in the directine of motion.
The force
( )F

---------time (t) graph is shown in figure. The final speed of the body is _________
(A) 9.25 ms
-
1
(B) 5 ms
-
1
(C) 14.25 ms
-
1
(D) 4.25 ms
-
1
2 4 4.5 6.5
F (N)
4
2.5
t (s)
F
t
0
F0
a a a a
Page 10

Laws of Motion Notes and MCQs

Laws of Motion Notes and MCQs

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