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Dnyansagar AIEEE / MHT-CET Excellent Notes - Physics I

Std. - 12th (Science) MHT-CET
QUESTIONS 1)
A car is taking a turn on a level road. It
may be thrown outwards because of the:
a) weight
b) lack of centripetal force
c) reaction of the ground
d) frictional force
2)
A body of mass m is moving with
velocity v in uniform circular motion.
The work done by the centripetal force
in moving through half the circular
path is :
2
m 2
m
2
a)
r
b)
r
r
r
2
m
c)
zero
d)
2 r
r
3)
In uniform circular motion :
a)
Both velocity and acceleration re
constant
b)
Acceleration and speed are constant
but velocity changes
c)
Both accleration and velocity
changes
d)
Both decreases and speed is constant
4)
The uniform circular motion is
accelerated motion, because
a) the motion accelerates due to the
change in velocity
b) the motion accelerates due to the
change in angular velocity
c) the motion accelerates due to the force
d) all of these
5)
The passengers in car are thrown
outwards when the car negotiates a curve, but the cyclist bends inwards
while negotiating the same curv e. This
happens because :
a) the car is heavier than the cycle
b) cyclist counteracts the centrifugal
force, which throws the passengers in
the car outwards
c) the cyucle has two wheels while the car
has four wheels
d) the cycle moves slower than the cars.
6) Torque produced by the centripetal
force
F
in circle of radius r is given
C
by :
a)
r
F
b)
F
r
C
C
c)
zero
d)
None of these
7)
The angle between radius vector and
centripetal acceleration is :
a)
b)
2
c)
2
d)
8)
The angular displacement in circular
motion is -
a) dimensional quantity
b) dimensionless quantity
c) unitless quantity and imensionless
quantity
d) unitless quantity

Ans -

(1 - b) (4 - a) (7 - d)

(2 - c) (5 - b) (8 - b)

(3 - c) (6 - c)

CIRCULAR MOTION

DNYANSAGAR A. Nagar 12

Dnyansagar AIEEE / MHT-CET Excellent Notes - Physics I

Std. - 12th (Science) 9) A particle moves along a circular path
of constant radius. The magnitude of its
acceleration is :
a) uniform
b) variable
c) zero
d) such as cannot be predicted from the
10)
given information
A body of mass m is moving in a
horizontal circle of radius r . If the
centripetal force is F, the kinetic energy
of the body is :
F.r
a)
2 b)
F . r
2
F. r
c)
d)
F.r
2
11)
A particle of mass m moving in a
horizontal circle of radius r with a
uniform speed v. When it moves from
one point to diametrically oppsite point
its:
a)
Kinetic energy changes by mv 2 /4
b)
Momentum does not changes
c)
Momentum changes by 2mv
d)
Kinetic energy changes by mv 2
12)
The direction of angular displacement
in U.C.M. is given by
a) left hand rule
b) right hand thumb rule
c) right handed screw rule
d) either a or b
13)
A particle is moving on a ciruclar path
with constant speed. Which of the
is true?
c) It possesses tangential acceleration
d) It does not possess tangential velocity.
14)
A particle is acted upon by a force of constant magnitude which is always
perpendicular to the velocity of the
particle. The motion takes place in a
plane. It follows that :
a) Its velocity is constant
b) Its acceleration is constant
c) Its motion is linear
d) Its motion is circular
15)
The rate of change of angular velocity
w.r. to t in uniform circular motion is a
b) angular acceleration ( )
c) angular speed
d) angular displacement
16)
What is the relation between tangential
acceleration a T and the centripetal
acceleration a
during non uniform
c
circular motion?
a)
a
must be greater than a
T
c
b)
a T must be less than a c
c)
a
must be equal to a c
T
d)
None of the above relations is true.
17)
A body of mass m is moving with
uniform speed in a horizontal circle of
k
radius r under a centripetal force
,
2
r
where k is a constant. The K.E. of body
is :
k 2
k
a)
b)
r
2 r
k
k
c)
d)
2
r
r

Ans -

(9 - d) (12 - d) (15 - b)

(10 - a) (13 - a) (16 - d)

(11 - c) (14 - d) (17 - b)

CIRCULAR MOTION

DNYANSAGAR A. Nagar 13

Dnyansagar AIEEE / MHT-CET Excellent Notes - Physics I

Std. - 12th (Science)

18) A satellite of earth is revolving with

uniform speed v. If gravitational force

suddenly disapperas, the satellite will :

a) Continue tomove wit velocity v along

the orginal orbit

b) Moves with velocity v tangential to

orbit

c) Fall down with increasing velocity

d) Ultimately come to rest somewhere n

the orginal orbit

19) The infinitesimal angular displacement

of a particle performing uniform

circular motion is a vector because

it obeys the cumulative and associative

it do not obeys the laws of vector

it do not obeys the laws of

multiplication of vectors

d) all of these

20) Which of the following statements about the uniform rotatory motion along a circular path is true?

a) Linear veolcity is uniform when angular velcoity is uniform

b) Magnitude of acceleration is constant

c) Acceleration is directed along the tangent to the ciruclar path

d) None of the above statement is correct

21) A body of mass 10 g tied to a string 20

cm long is whirled in horizontal circle.

If the string breaks under a force of 20 N. What can be the maximum angular
speed?
a)
b)
c)
d)
22)
A particle revolves round the circular
path
with constant speed. The
acceleration of particle is :
a) Along the circumference of the circle
b) Along the tangent
d) Zero
23)
If a particle goes round the circle once
in a time period T, then the angular
velocity will be
a)
2
t
b)
T / 2
c)
2 /T
d)
/T
24)
What determines the nature of the path
followed by the particle?
a)
Speed
b)
Velocity
c)
Acceleration
d)
None of the above
25)
For a body moving in circular path of
radius r with uniform speed the angle
of banking is given by :
2
2
a)
b)
r.g
tan -1 r.g
2
c)
d)
None of these
r

Ans -

(18 - b) (21 - b) (24 - b)

(19 - a) (22 - c) (25 - b)

(20 - b) (23 - c)

CIRCULAR MOTION

a) DNYANSAGAR
b)
c) A. Nagar 14

Dnyansagar AIEEE / MHT-CET Excellent Notes - Physics I

Std. - 12th (Science)

26) A wheel rotates about an axis passing through the centre and perpenducular to the plane with slowly incresing angular speed. it has :

b) Tangential velocity and radial acceleration

c) Tangetial velocity and tangential acceleration

d) Tangential velocity and acceleration having both tangential and radial components

27) The relation between linear velocity and angular velocity of a body moving in circle in vector form is

 a) v r b) v r
 c) v d) / r r v

28) Which of the following statements about the centripetal and centrifugal forces is

correct?

Centripetal force balances the

centrifugal force

b) Both centripetal force and centrifugal

force act on the same body

c) Centripetal; force is directed opposite

to the centrifugal force

d) Centripetal force is experienced by the

observer at the centre of the ciruclar

path described by the body.

29) A body of 1kg is tied to the end of a string

1 m long and whirled in a vertical circle

with a constant speed of 4 m s -1 . The

tension in the string is 6.2 N. when the stone is :

a) at the top of the circle

b) at ther bottom of the circle c) half-way down the circle
d) None of the above
30)
The work done by the centripetal force
F
when a body completes one revolution
around a circle of radius R is :
a)
2 RF
b)
2 RF
c)
RF
d)
Zero
31)
What is the angular displacement of the
minute hand in 20 minutes?
a)
b)
c)
d)
3
32)
A scooter is going around a circular
10 ms -1 . What is the angular speed of the
scooter?
a)
-1
b)
-1
c)
-1
d)
33)
A body of mass m tied to a string of
length r is at its lowest position. What
should be the minimum speed given to
it
so as just to complete one revlolution?
a)
gr
b)
3gr
c)
5gr
d)
7gr
34)
Which
of
the
following
remains
constant in UCM?
a) Speed
b) Kinetic energyKinetic energy
c) Angular momentum
d) All of these

Ans -

(26 - d) (29 - a) (32 - c)

(27 - a) (30 - d) (33 - c)

(28 - c) (31 - b) (34- d)

CIRCULAR MOTION

DNYANSAGAR a) A. Nagar 15

Dnyansagar AIEEE / MHT-CET Excellent Notes - Physics I

Std. - 12th (Science) 35)
A motor car is travelling 20 m/s on a
increases its speed at the rate of 1 m/s 2 ,
then its acceleration will be
c) Instantaneous angular velocity
d) None of the above
41)
a)
2
b)
2
2
2 m/s
3 m/s
c)
2
d)
2
2 m/s
3
3 m/s
36)
To enable a particle describe a circular
path, what should be the angle between
its velocity and acceleration?
A simple pendulum has a length l. What
minimum velocity should be imparted
to its bob at the mean position so that
the bob reaches a height equal to above
the point of suspension :
a)
gl
b)
5 gl
l
a)
0 0
b)
45 0
c)
2 gl
d)
g
c)
90 0
d)
180 0
42)
37)
A body is to be slided without fricition
along an inclined plane of height h so
Scalar product of radius vector and
tangential velocity is :
a)
zero
b)
rv cos
that it loops the loop of radius r at the
c)
rv sin
d)
rv
bottom. The value of height is :
DNYANSAGAR
43)
Centrifugal force is pseudo force
a)
h = 2r
b)
h = 4r
because
5
c)
h = 5r
d)
h =
a)
2 r
it is not provided by any real force but
it arises due to accelerated frame of
38)
Earth is slightly bulge at equator so
A. Nagar
reference
shape of earth is oblate spheroid. This
b)
origin can not imaginary
is because at equator :
c)
its direction is outwards along radius
a) Gravitational force is maximum
d)
b) Angular velocity is maximum
its magnitude is equal to centripetal
force
c) Centrifugal force is maximum
44)
d) Above statement is worng
39)
If a stone is tied to a string and whirled
A flywheel rotates at a constant speed of
3000 rpm. The angle described by the
shaft in radian in one second is :
in a circle, then the centripetal force
would provides
a)
2
b)
30
c)
100
d)
3000
a) tension in the string
b) mass of the string
c) weight of string
d) mass of stone
Ans -
40)
All the magnitudes of which of the
following can be treated as vectors?
a) Angular displacement
b) Average angular velocity
(35 - c)
(38 - c)
(41 - b)
(44 - c)
(36 - c)
(39 - a)
(42 - a)
(37 - d)
(40 - c)
(43 - a) CIRCULAR MOTION 16

Dnyansagar AIEEE / MHT-CET Excellent Notes - Physics I

Std. - 12th (Science) 45)
A stone tied to string is whirled then the
string breaks at certain speed because:
d)
None of the above
51)
A cyclist moves round a circular road
a) Gravitational force is maximum
b) The required centripetal force is
greater than tension sustainable by the
string
c) Required centripetal force is equal to
tension in the string
of radius 50 metres. If the coefficient of
friction between the tyres and road is
0.2, the maximum velocity with which
he can go round without skidding is
(g = 10m s -2 ) :
a)
5 m s -1
b)
10 m s -l
d) Centripetal force is equal to weight
c)
20 m s -1
d)
7.5 m s -1
46)
The driver of a car travelling at velocity
52)
v suddenly sees a broad wall in front of
him at a distance a . He should
A stone of mass m is tied to a string of
length L, and rotated in a circle with
a)
brake sharply b)
turn sharply
constant speed v, if the string is released
the stone flies :
c)
both a and b d)
none
a)
47)
The angular speed of the hour hand of
b)
the clock is :
a)
b)
DNYANSAGAR
A. Nagar
c)
Tangentially
2
-1
d)
With an acceleration mv /L
2
2
-1
53)
A scooter is going around a circular
c)
track with a speed of 20 ms -1 . The radius
d)
None of the above
of
the ciruclar track is 50m. The angular
48)
In a circus a motor-cyclist rides along a
velocity of the scooter is :
circular track of radius r in a vertical
a)
-1
b)
circle, the minimum speed at the highest
point in order to avoid a fall is:
c)
d)
54)
A motor cyclist moves round a curve at
a)
2 gr
b)
5 gr
a
certain speed. He doubles his speed.
c)
3 gr
d)
gr
49)
The centripetal force is real force which
provides with the real interacting force
of
The ratio of the tangents of the angles
by which he leans with vertical in two
cases is :
a)
1:2
b)
4:1
a) mechanical
c)
1: 4
d)
2:1.
b) electrical
c) magnetic or gravitational
d) All of these
Ans -
50)
The angular speed of the munute hand
of the clock in degrees per second is :
a) 0.01
b) 0.1
(45 - b)
(48 - d)
(51 - b)
(54 - c)
(46 - a)
(49 - d)
(52 - c)
(47 - d)
(50 - b)
(53 - a)
c) 1.0
17
CIRCULAR MOTION

Dnyansagar AIEEE / MHT-CET Excellent Notes - Physics I

Std. - 12th (Science)

55)

56)

A spirit level is placed at the edge of a

turn table along its radius. The bubble

will be

a) at the centre of the container

b) at the outer edge of the container

c) at the inner edge of the container

d) will oscillate about the centre of the

container

One radian is approximately equal to :

 a) 180 0 b) 57 0 c) 90 0 d) 360 0

57)

58)

A particle covers equal distances around

a circular path in equal intervals of

time. It has uniform non zero rate of

change of :

linear displacement

angular displacement

linear velocity

angular velocity

When a cyclist takes a circular turn he leans:

 a) inward b) outward c) backward d) forward.

59)

A ball of mass 0.25kg attached to the end

of a string of length 1.96 m is moving in a horizontal circle. The string will break, if the tension is more than 25 N. What is the maximum speed with which the ball can be moved?

 a) 14 m/s b) 3 m/s c) 3.92 m/s d) 5 m/s

60)

In a vertical circle of radius r, at what point in its path, particle has tension equal to zero?

a) Highest point

b) Lowest point c) Any point
d) Horizontal point
61)
A particle is moving around a circular
path with uniform angular speed . The
radius of the circular path is r. The
acceleration of the particle is :
a)
2 /r
b)
2 /r
c)
r 2
d)
r 2
62)
A stone of mass m tied to a string is
rotated in a circle of radius r with
angular velocity . The force of tension
trying to break the string is :
2
m
a) mrw 2
b)
r
m
c)
d)
None of these.
2
r
63)
The string of a conical pendulum will
become horizontal when :
a)
Speed of revolution is zero
b)
Speed of revolution is almost
infinite
c)
Speed of revolution is low
d) Speed of revolution is very low
64)
A particle moves along a circular path
of radius r with uniform speed . The
angle described by the particle in one
second is given by :
a)
r -1
b)
-1 r
c)
r -2
d)
2 r

Ans -

(55 - c) (58 - a) (61 - c) (64 - a)

(56 - b) (59 - a) (62 - a)

(57 - b) (60 - a) (63 - b)

CIRCULAR MOTION

DNYANSAGAR
a) b) c) d) A. Nagar 18

Dnyansagar AIEEE / MHT-CET Excellent Notes - Physics I

Std. - 12th (Science)

Centrifugal machines make use of which

of the following forces for their action:

a) gravitational force

b) frictional force

c) centrifugal force

d) viscous force

66) A motor cycle is going on an over bridge of radius R. The driver maintains a constant speed. As motor cycle is ascending on the over bridge, the normal force on it :

65)

67)

68)

69)

70)

a) Increases

b) Decreases

c) Remains the same

d) Fluctuates - erratically

The angular acceleration of a particle

moving along a circular path with

uniform speed is :

a)

uniform but non zero

zero

variable

such as cannot be predicted from the

given information

d)

Cream is separated from the milk

because:

a) cream is heavier than skimmed milk

b) cream is 1ighter than skimmed milk

c) cream is more viscous

d) None of the above.

What determines the nature of path

followed by the particle?

a) Speed

b) Velocity

c) Acceleration

d) None of these

A body of mass 10 kg is moving in a circle of radius 1 m with an angular

velocity of 2 rad/s. The centripetal force is

a) 10 N

b)

40 N c) 30 N
d)
20 N
71)
A particle is describing the circular
path of radius 10m every 2s. The average
angular speed of the particle, during 4s
is :
c) 20
d) None of the above
72)
A man going on a cycle round a circular
track of length 34.3 metres completes
one round in 22 sec. The angle through
which he leans inward is :
a) 30°
b)
60°
c)
45°
d)
20°
73)
If a particle moves in a circle describing
equal angles in equal times in aplane
about a fixed point, its velocity vector :
a)
Remains constant
b)
Changes in magnitude
c)
Changes in direction
d)
Changes both in magnitude and
74)
direction
A particle is moving along a circular
path with uniform speed. What is the
angle between its instantaneous velocity
and acceleration?
a)
0 0
b)
45 0
c)
90 0
d)
180 0

Ans -

(65 - c) (68 - b) (71 - d) (74 - c)

(66 - b) (69 - b) (72 - c)

(67 - b) (70 - d) (73 - c)

CIRCULAR MOTION

DNYANSAGAR c) b) A. Nagar 19

Dnyansagar AIEEE / MHT-CET Excellent Notes - Physics I

Std. - 12th (Science) 75)
The string of a conical pendulum will
become horizontal when:
a) speed of revolution is zero .
b) speed of revolution is almost
infinite
c) speed of revolution is low
d) speed of revolution is very high
76)
An aeroplane is taking a turn in a
horizontal plane. While doing so, it
a)
remains horizontal
b)
inclines inwards
c)
inclines outwards
d)
makes wings vertical
77)
In
half
period of revolution
displacement and the distance covered
is :
a)
2r,
r
b)
2
r, 2r
c)
r, 2r
d)
zero,
2 r
78)
A car is going around a circle of radius
R 1 with constant speed. Another car is
going around a circle of radius R 2 with
constant speed. If both a them take same
time to complete the circles, the ratio
of their angular speeds will be :
a)
R R
/
b)
R 1 / R 2
1
2
c) R 1 2 / R 2 2
d)
1
79)
An iron ball is moving from rim to rim
via lowest point at the bottom of a small
hemispherical bowl of radius 10cm. The
velocity with which the ball passes from
the lowest position is : (g = 9.8 m s -2 )
a)
14 m s -1
b)
140m s -1
c)
1.4 m s -1
d)
0.7 m s -l
80)
A motor cyclist rides around the well
with a round vertical wall and does not
fall down while riding becuase :
a) The force of gravity disappears
b) The frictional force of the wall balances his weight
c) He loses weight some how
d) The force exerted by the surrounding
81)
A car moves on a circular road. It
describes equal angles about the centre
in equal intervals of time. Which of the
of the car is true?
a) Velocity is constant
b) Magnitude of velocity is constant but
direction changes
c) Both magnitude and direction of
velocity change
d) Velocity is directed towards the centre
of the circle.
82)
A car is moving on a curved bridge of
radius r with velocity v. The maximum
velocity with which it can move round
it without leaving the bridge at the
highest point is :
a)
v
gr
b)
v
5 gr
c)
v
2 gr
d) v =
gr
83)
A car is moving along the horizontal
banked curved road. At banked curve
a) equal to weight
b) greater than weight
c) less than weight
d) less than or equal to weight

Ans -

(75 - b) (78 - d) (81 - b)

(76 - b) (79 - c) (82 - a)

(77 - c) (80 - b) (83 - b)

CIRCULAR MOTION

DNYANSAGAR

A. Nagar 20

Dnyansagar AIEEE / MHT-CET Excellent Notes - Physics I

Std. - 12th (Science)

84)

85)

86)

87)

88)

89)

A particle is revolving in a circle,

clockwise in the plane of the paper. The angular acceleration is directed :

a) Towards the centre in the plane of the paper

b) Radially outwards in the plane of the paper

c) Perpendicular to the plane of the paper

d) Vertically in the plane of the paper

A particle is moving along a circular path with uniform speed. Throgh what

angle does its angular velocity change when it completes half of the circular path?

a)

c)

One kg stone tied to a metre long string

is whirled in a vertical circle with 4 m s -1 . The tension is 6 N at (g = 10m s -2 ):

a) top of circle

b) bottom of circle

c) half way down

d) None of these.

A body moving in a circular path with constnt speed has :

a) constant retardation

b) variable acceleration

d) constant acceleration

A bucket full of water is rotated in a vertical circle. The water does not spill

because the weight of water:

a) provides the necessary centripetal force

b) provides the centrifugal force

c) provides the viscous force

d) cancels the force of surface tension

If a body of mass 1000 gm is tied to free end of string of length 100 cm and whirled in a horizontal circle in a

0 0

180

0

b)

d)

45 0

36

0 second, then the tensionin the string
will be
a)
4
2
N
b)
2
2 N
c)
3
2
N
d)
2 N
90)
If the fingers of the right hand are
curled in the sense of motion of the
particle performing circular motion
then the outstretched thumb gives the
direction of :
a) Angular velocity, Angular
acceleration
b) Tangential velocity
c) Tangential acceleration
d)
Linear velocity
91)
The length of the second hand of a watch
is 10mm. What is the change in the
angular speed of the watch after 15
seconds?
a)
Zero
b)
(10
/2) mm
s -1
c)
(20/
) mm s
-1
d) 10
2 mm s -1
92)
For a car moving along circular road of
radius r and with coefficient of friction
between the tyres and the road, the
maximum velocity without skidding is:
a)
v
rg
b)
v
rg
c)
v 2 rg
d)
None of these.

Ans -

(84 - c) (87 - b) (90 - a)

(85 - a) (88 - a) (91 - a)

(86 - a) (89 - a) (92 - b)

CIRCULAR MOTION

DNYANSAGAR

A. Nagar 21

Dnyansagar AIEEE / MHT-CET Excellent Notes - Physics I

Std. - 12th (Science)

An important consequence of

centrifugal force is that the earth is :

a) Spheroid

b) Sphere

c) Oblate spheroid

d) Circular

94) A coin kept on a horizontal rotating disc has its centre at a distance of 0.25 m from the aixs of rotationof the disc. If is 0.2, then the angular velocity of the disc at which the coin will slip off, ( g= 9.8 m/

93)

95) Two satellites are going around the

earth at a height of 200 km and 300 km

respectively. If angular speed of both is

same, the centripetal acceleration will be :

a) same for both

b) more for the first

c) more for the second

d) dependent on the mass of the satellite

96) A scooterist is moving round a circular track of radius 480 m. The track is 1 m wide. If his speed is 72 km/hour, how much the outer edge of track is lifted to bank the track for him? (g = 10 m s -2 )

 a) 10cm b) 50cm c) 8.3cm d) 4.1cm

97) The angular velocity of a wheel is 70 rad/ s/ If the radius of the wheel is 0.5m, then its linear velocity will be :

 a) 10 m/s b ) 35 m/s c) 20 m/s d) 70 m/s

98) A pendulum bob on a 2 m string is displaced 60 0 from the vertical and then released. What is the speed of the bob as it passes through the lowest point in
its path?
a)
2 m/s
b)
9.8 m/s
c)
4.43 m/s
d)
2 m/s
1/
99)
A particle covers equal distances around
a
circular path in equal intervals of
time. Which of the following quantities
connected with the motion of the
particle remains constant with time?
a)
Displacement b) Velocity
c)
Speed d) Acceleration
100)
A body is tied to a string and is whirled
in the vertical circle of radius r. The
velocity of the body is maximum :
a) at the highest point
b)
at the lowest point
c)
at a point in level with the centre
horizontally
d) None of the above.
101)
A particle moves in a circular path 0.4m
in
radius with constant speed. If particle
makes 5 revolutions in each second of
its motion the speed of the particle is :
a)
10.6 m/s
b)
12.56 m/s
c) 11.2 m/s
d)
13.6 m/s
102)
If a cyclist doubles his speed while
negotiating a curve, how does the
tendency to overturn vary?
a) Remains unchanged
b) Doubled
c) Halved

Ans -

(93 - c) (96 - c) (99 - c) (102 - d)

(94 - b) (97 - b) (100 - b)

(95 - c) (98 - c) (101 - b)

CIRCULAR MOTION

DNYANSAGAR

A. Nagar 22

Dnyansagar AIEEE / MHT-CET Excellent Notes - Physics I

Std. - 12th (Science) 103)
curvature is 50 m. The outer edge is
above the lower edge by a distance of 1.5
m. This road is most suited for the
velocity
a)
2.5 m/s
b)
8.57 m/s
c)
6.5 m/s
d)
3.5 m/s
104) A small body of mass m slides down a
hemispherical smooth bowl from the
rim to the bottom. The velocity of the
body at the bottom is :
a)
2 gr
b)
5 gr
c)
gr
d)
None of these.
105)
A particle moves in a circle of radius 25
cm
at two revolutions per second, the
aceleration of particle in m/s
2
is:
a)
2
b)
4
2
c)
8 2
d)
2 2
106)
The radius of the circular path of
particle is doubled but its frequency of
rotation remains unchanged. If the
initial centripetal force be F, then the
final value of the centripetal force will
be :
a)
F
b)
2F
c)
4F
d)
F/2
107)
A particle P is moving in a circle of
radius a with uniform velocity v.C. is
centre of the circle and AB is adiameter.
The angular velocity of P about A and C
are
in the ratio :
a)
1
:
1
b)
2 :
1
c)
1
:
2
d)
4 :
1
108)
A particle of mass m is rotating by means
of a string in a vertical circle. The
difference in the tensions at the bottom
and the top would be:
 a) 6 mg b) 4 mg c) 2 mg d) 3 mg.

109) A car is moving in a circular horizontal track of radius 10 m, with constant speed 10 m/s. A bob is suspended from roof of car with rod. Angle made by rod with vertical : (g = 9.8 m/s 2 )

 a) Zero b) 45 0 c) 30 0 d) 60 0

110) A can filled with water is revolved in vertical circle of radius 4 m and water just does not fall down at the highest point. The time period of revolution is(g= 9.87 m s -2 ) :

a)

c)

1 sec

4 sec

b)

d)

2sec

8 sec

111) A simple pendulum of length 1 m, the

bob performs circular motion in

horizontal plane if its string making an

with the vertical, then the

period of rotation of the bob will be ( g

angle 60

0

2

= 10 m/s )

 a) 2 s b) 1.4 s c) 1.98 s d) 4 s

112) A cyclist turns around a curve at 40 km/ hr. If he rounds the curve at double speed, his tendency to overturn is :

 a) Doubled b) Halved c) Tripled d) Quadrupled

Ans -

(103 - b) (106 - b) (109 - b) (112 - d)

(104 - a) (107 - c) (110 - c)

(105 - b) (108 - a) (111 - b)

CIRCULAR MOTION

DNYANSAGAR A. Nagar 23

Dnyansagar AIEEE / MHT-CET Excellent Notes - Physics I

Std. - 12th (Science) 113) A disc revolves in a horizontal plane at
the rate of 210 r.p.m. A coin placed at a
distance of 2cm from the axis of rotation
just remains at rest on the disc. The
coefficient of friction between the disc
and coin is (g = 10 m s- 2 )
length 1 m, then the angle made by the
rod with thetrack will be (g = 10 m/s 2 )
a)
zero
b)
30
0
c)
45 0
d)
60
0
118) The string of a simple pendulum is
horizontal at a given height and is
a)
0.97
b)
0.5
released. The tension in the string at the
lowest point is :
c)
0.35
d)
1
a)
T = mg
b)
T = 2 mg
114)
A person with his hands in his pocket is
skating on ice at the rate of 10 m/s and
describes a circle of radius 50 m. What
is his inclination to the vertical?
c)
T = 3 mg
d)
T = 4 mg
119)
(g = 10 m/s 2 )
In an atom two electrons move round the
nucleus in circular orbits of radii R and
4R respectively, the ratio of time taken
by them to complete one revolution is :
F
F
1
G J I
1
G J I
a) tan
H 1
b) tan
H 3
1
8
2
5
a)
b)
DNYANSAGAR
A. Nagar
4
1
F
F
1
G J I
1
G
J I
tan
H 1
tan
H 1
4
1
c)
d)
5
10
c)
d)
1
8
115)
A proton revolves round a circular path
120) A motor car is travelling at 30 m s -1 on
of radius 0.1 m. If it is acted upon by a
a circular curve of radius 500 m. It is
force 4 x 10 -13 N to keep it moving, the
increasing its speed at the rate of
angular velocity of proton is
2 m s
-2
, what is its acceleration?
(m
p = 1.6 x 10 -27 kg):
a)
2 m s -2
b)
1.8 m s -2
a)
5 x 10 7 rad s -1
b)
5 x 10 7 rad s -1
c)
2.7 m s -2
d)
none of these
c)
d)
116)
Amotor cyclist moving with velocity of
72 km/hr on a flat road takes a turn on
curvature of the road is 20 m. In order
121) In a circus a rider rides in a circular
track of radius R in vertical plane. The
minimum velocity at the highest point
of the track is :
a)
2gR
b)
3gR
to avoid skidding, he must bend w.r.t. the
vertical plane by a n angle greater
than : (g = 10 m/s 2 )
c)
2gR
d)
gR
a)
=
tan
-1
(6)
b)
= tan -1 (25.92)
Ans -
c)
= tan -1
(2)
d)
= tan -1 (4)
117)
A car is moving in a horizontal circular
track of radius 10 m with a constant
speed 10m/s. If a bob is suspended form
the roof of the car by light rigid rod of
(113 - a)
(116 - c)
(119 - d)
(114 - c)
(117 - c)
(120 - c)
(115 - a)
(118 - c)
(121 - d)
24
CIRCULAR MOTION

Dnyansagar AIEEE / MHT-CET Excellent Notes - Physics I

Std. - 12th (Science)

122)

A train is safely negotiating a curve of

radius 500 m at a speed of 54 m hr -1 . By how much should the outer rail be raised, if the distance between the two rails is 1.5 m? (g = 10 m s -2 )

 a) 6.75 cm b) 15 cm c) 4.5 cm d) 2.5 cm

123)

124)

125)

126)

Kinetic energy of a body moving in

vertical circle is

a) constant at all points on a circle

b) different at different points on a circle

c) zero at all the point on a circle

d) negative at all the points

A motor car is travelling at 20 m/s on a

circular curve of radius 100 m. It is

increasing its speed at the rate of 5 m/s

what is its acceleration?

2

a)

c)

When a particle is moved in a vertical

circle

a)

2 m/s 2

4 m/s 2

b)

d)

6.4 m/s 2

9 m/s 2

it has constant radial and tangential

acceleration

b) it has variable tangential and radial acceleration

c) it has only constant radiual acceleration

d) it has only constant tangential

acceleration A ball of mass 0.25 kg attached to the end

of a string of length 1.96 m is moving in

a horizontal circle. The string will

break if the tension is more than 25N.

what is the maximum speed with which the ball can be moved?

 a) 14 m/s b) 4 m/s c) 3.92 m/s d) 5 m/s

127)

A particle of mass 100 g is tied to one end of string of length 1 m. It rotates in a vertical circle. When the string makes an angle of 60 0 with the vertical, its
velocity is 2 m/s. The tension in the
string in this position : (g = 9.8 m/s 2 )
a)
0.4 N
b)
0.89 N
c)
0.09 N
d)
0.98 N
128)
A weightless thread can support tension
upto 30 N.A. stone of mass 0.5 kg is tied
to it and is revolved in a circular path
of radius 2m in a vertical plane. If g =
10 m/s 2 , then the maximum angular
velocity of the stone will be :
a)
b)
c)
d)
129)
A pilot of mass 81 kg loops the loop with
is 0.5 km then the force with which the
pilot is pressed into the seat at the
highest point of the loop, is
a)
3.15 x 10
2
N
b)
c)
8.10 x 10
2
N
d)
zero
19.35 x 10 2 N
130) A mass of 100 g is tied to one end of a
string 2 m long. Thebody is revolving
in a horizontal circle making a
maximum of 200 rpm. The outer end of
string is fixed at the centre of
revolution. The maximum tension the
string can bear is approximately :
a)
8.76 N
b)
8.94 N
c)
89.42 N
d)
87.64 N

Ans -

(122 - a) (125 - b) (128 - a)

(123 - b) (126 - a) (129 - a)

(124 - b) (127 - b) (130 - d)

CIRCULAR MOTION

DNYANSAGAR A. Nagar 25

Dnyansagar AIEEE / MHT-CET Excellent Notes - Physics I

Std. - 12th (Science) 131) A stone of mass 16 kg is attached to a
string 144 m long and is whirled in a
horizonal circle. The maxmium tension
the string can stand is 16 newton. The
maximum velocity of revolution that can
be given to the stone without breaking
it, will be :
a)
20 ms -1
b)
16 ms -1
c)
14 ms -1
d)
12 ms -1
132) Assuming the coefficient of friction
between the road and tyres of a car to be
0.5 the maximum speed with which the
car can move round the curve of 40 m
unbanked should be : (g = 9.8 m/s 2 )
a)
25 m/s
b)
19 m/s
c)
14 m/s
d)
11 m/s
133) A weightless thread can bear tension
upto 3.7 kg wt. A stone of mass 500g is
tied to it and revolved in a circular path
of radius 4 m in a vertical plane. If g =
10 ms -2 , then the maximum angular
velocity of the stone will be :
a)
b)
c)
d)
21
134)
A boy on a cycle pedals around a circle
of radius 20 m at a speed of 20 m/s. The
combined mass of boy and the cycle is
90 kg. The angle that the cycle makes
with vertical so that he may not fall :
(g = 9.8 m/s 2 )
a) 60.50
0
c)
63.90
0
b) 26.12
0
d)
30.00
0
135) A fighter plane is moving in a vertical
circle of radius r. Its minimum velocity
at the highest point of the circle will be:
a)
3gr
b)
2gr
c)
gr
d)
gr / 2
136)
If a body of mass 0.1 kg tied with a string
of length 1 m, is rotated in vertical circle, then the energy of the body at the
highest position will be (g = 9.8 m/s 2 )
a)
2.45 J
b)
1.25 J
c)
3.45 J
d)
4.45 J
137)
The maximum velocity at the lowest
point, so that the string just slacks at
highest point in a vertical circle of
a)
gl
b)
3gl
c)
5gl
d)
7gl
138)
The second hand of a watch has length
6cm. Speed of end point and magnitude
of difference of velocities at two
perpendicular position will be :
a)
6.28 and 0 mm/s
b)
8.88 and 4.44 mm/s
c)
8.88 and 6.28 mm/s
d)
6.28 and 8.88 mm/s
139) A 500 kg car takes round turn of radius
50m with a velocity of 36 km/h. The
centripetal force is :
a)
250 N
b)
750 N
c) 1000 N
d)
1200 N
140)
A hollow sphere has radius 6.4 m.
Minimum velocity required by motor
cyclist at bottom to complete the circle
will be :
a)
17.7 m/s
b)
12.4 m/s
c)
10.2 m/s
d)
16.0 m/s

Ans -

(131 - d) (134 - c) (137 - c) (140 - a)

(132 - c) (135 - c) (138 - d)

(133 - a) (136 - a) (139 - c)

CIRCULAR MOTION

DNYANSAGAR A. Nagar 26

Dnyansagar AIEEE / MHT-CET Excellent Notes - Physics I

Std. - 12th (Science) 141)
A stone of mass 1 kg tied to one end of a
string of length 1m, is whirled in a
horizontal circle with a uniform
angular velocity of 2 rad/s. The tension
(in N) in the string is :
1
a)
2
b)
2
1
c)
4
d)
4
142)
A body of mass 2 kg attached to a cord
and whirled in a vertical circle of radius
2 m. The minimum speed at the bottom
of the circle so that the cord will not
slacken when the body rounds the top of
the circle will be ( g = 10 m/s 2 )
a)
10 m/s
b)
6.3 m/s
c)
7 m/s
d)
5 m/s
143) When angular velocity of a uniform
rotating body has increased thrice, the
resultant of forces applied to it
increases by 60 N. Find the acceleration
of the body, in two cases if the mass of
the body is 3 kg :
a) 2.5 m/s 2 , 7.5 m/s 2
b) 7.5 m/s 2 , 22.5 m/s 2
c) 5 m/s 2 , 45 m/s 2
d) 2.5 m/s 2 , 22.5 m/s 2
144)
A particle is acted upon by a force of
constant magnitude which is always
perpendicular to the velocity of the
particle, the motion of the particle takes
place in a plane. It follows that :
a) its velociyt is constant
b) in moves in a straight line
c) its kinetic energy is constant
d) its acceleration is constant
145)
The earth (mass = 6 x 10 24 kg) revolves
round the sun with angular velocity
1.5 x 10 8 km. The force exerted by sun
is:
a) 3.6 x 10 21 N
b)
3.6 x 10 -21 N c) 36 x 10 21 N
d)
3.6 x 10 9 N
146)
Two racing cars of masses m 1 and m 2 are
moving in circles of a radii r 1 and r 2
respectively. Their speeds are such that
they each make a complete circle in the
same length of time t. The ratio of the
angular speed of the first to the second
car is :
a)
m 1 : m 2
b)
1
:
1
c)
r 1 : r 2
d)
m 1 r 1 : m 2 r 2
147)
Breaking tension in the string is 80 N. A
body of mass 0.1 kg is attached to it and
whirled in circle of radius 0.5m. What
will be maximum period of revolution
before string breaks?
a)
s
b)
s
20
c)
s d)
s
5
10
148) A tube of length L is completely filled
with an incompressible liquid of mass
m
and closed at both ends. The tube is
then rotated in horizontal plane about
one of its end with uniform angular
speed . What is force exerted by liquid
at
the other end?
2
2
mL
mL
a)
b)
2
4
2
mL
c)
2 d)
mL
8
v

Ans -

(141 - c) (144 - c) (147 - b)

(142 - a) (145 - c) (148 - a)

(143 - d) (146 - a)

CIRCULAR MOTION

DNYANSAGAR

A. Nagar 27

Dnyansagar AIEEE / MHT-CET Excellent Notes - Physics I

Std. - 12th (Science) 149)
The maximum speed with which a car
can be safely driven along a curved road
of radius 30 m and banked at 30 0 with
horizontal :
a)
130 m/s
b)
14.00 m/s
c)
1.303 m/s
d)
13.03 m/s
150) Find the maximum velocity for
overturning a car moved on a circular
track of radius 100m. The coefficient of
friction between the road and tyre is 0.2.
a)
0.14 m/s
b)
140 m/s
c)
1.4 km/s
d)
14 m/s
151) A coin placed on a rotating table just
slips when placed at a distance 4r from
the centre. On doubling he angular
velocity of the table. The coin will just
slip when distance from centre is equal
to :
a)
4r
b)
r
c)
2r
d)
r/4
152)
A particle of mass m describes a circle
of radius r. The centripetal acceleration
of the particle is 4/r 2 . What will be the
momentum of the particle?
a)
4 m/r
b)
2 m/r
c)
4 m /
d)
2 m/
r
r
153) A bucket tied at the end of a 1.6 long
string is whirled in a vertical circle
with constant speed. What should be the
minimum speed so that the water from
the bucket does not spill when the bucket
is at the highest position? (Take g = 10
m/s 2 )
a) 4 m/s
b) 6.25 m/s
c) 16 m/s
d) None of the above 154)
4
A
r
o
c
k
e
c
t
w
i
t
h
a
l
i
f
t
o
f
f
m
a
s
s
3
.
5
x
1
0
kg is blasted upwards with an initial
accleration of 10 m/s 2 . Then the initial
thrust of the blast is :
a)
3.5 x 10 5 N
b)
7.0 x 10 5
c)
14.0 x 10 5 N
d)
1.75 x 10 5 N
155) In an atom two electrons moves round
the nucleus in circular orbitsof radii R
& 4R respectively the ratio of the time
takan by them to complete one
revolution is:
a)
1/4
b)
4/1
c)
8/1
d)
1/8
*****

Ans -

(149 - d) (152 - d) (155 - d)

(150 - d) (153 - a)

(151 - b) (154 - b)

CIRCULAR MOTION

DNYANSAGAR A. Nagar 28
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