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AL-MC-Circular motion / p.1
1.
3.
(88-I-6)
(90-I-5)
A car of mass m travels into a region where the
track is an arc of a vertical circle of radius r. At the
bottom of this arc, the car travels at speed v. At this
A wheel rolls horizontally along the ground
position the vertical force exerted upwards by the
without slipping. The speed of the centre of
track on the car is
mass of the wheel is v. The instantaneous
speed of point P relative to the ground is
2
A.
B.
mv / r.
mg.
C.
mv 2 / r  mg.
D.
mg  mv 2 / r.
E.
mg  mv 2 / r.
zero.
B.
v.
C.
4.
2.
A.
2v .
D.
2v.
E.
4v.
(90-I-6)
A spring of unstretched length 10.0 cm, has
(89-I-8)
one end fixed to the ceiling. A mass is
suspended at the other end, and the extension
so produced is 3.0 cm. When the mass is set to
rotate in a horizontal circular path the length
of the spring is 16.0 cm. The angle between the
spring and the vertical is
A.
B.
A smooth conical container rotates about the axis
C.
AB as shown. A marble remains at rest relative to
D.
the container at a radial distance r from the axis. If
E.
the velocity of the marble is v, then v
A.
gr sin 30o .
B.
gr tan 30 o .
C.
gr / tan 30o .
D.
gr cos 30o .
E.
gr / cos 30 o .
2
is equal to
15o
30 o
45 o
60 o
75 o
AL-MC-Circular motion / p.2
5.
(91-I-6)
(1)
When moving towards the lowest point of its
path, the angular speed of the bob is
increasing.
(2)
The centripetal acceleration of the bob is
constant.
(3)
When the bob is at the lowest point, the
tension in the string equals the centripetal
The diagram shows part of the route of a
force.
roller-coaster in an amusement park. The cart
descends from H, completes a circular loop A and
A.
(1) only
moves to B. If the cart of passengers is to complete
B.
(3) only
the central circular track safely, what is the
C.
(1) and (2) only
minimum velocity of the cart at the bottom of the
D.
(2) and (3) only
circular track A? (Assume that there is no friction
E.
(1), (2) and (3)
between the cart and the track.)
7.
6.
(94-IIA-5)
A.
10 ms 1
A student whirls a small bucket of water in a
B.
20 ms 1
is the minimum speed of the bucket at the highest
C.
22.4 ms 1
D.
E.
vertical circle of radius 0.6 m. For no spilling, what
point of its path?
A.
2.45 ms-1
24.5 ms 1
B.
3.46 ms-1
C.
4.08 ms-1
30 ms 1
D.
4.90 ms-1
E.
5.77 ms-1
(93-I-8)
8.
(95-IIA-5)
A small object of mass 0.05 kg is released from
rest at the rim of a heavy, smooth semi-spherical
bowl of radius 10 cm. Find the force acting on the
object by the bowl when it passes the bottom of the
bowl.
The figure shows a small heavy bob P attached to a
fixed point A on the ceiling by a light inextensible
A.
0.5 N
string. The bob is pulled aside with the string taut
B.
1.0 N
and then released from rest. Which of the
C.
1.5 N
following descriptions is/are true?
D.
2.0 N
E.
2.5 N
AL-MC-Circular motion / p.3
9.
(95-IIA-6)
A.
5.0 ms
An aircraft flies along a horizontal circle of radius
B.
5.2 ms
10 km with a constant speed of 155 ms-1. Calculate
C.
5.4 ms
the angle between its wings and the horizontal.
D.
5.6 ms
E.
5.8 ms
A.
B.
C.
D.
E.
10.
11.5 o
12.0 o
12.5 o
13.0 o
13.5 o
12.
1
1
1
1
1
(97-IIA-5)
(96-IIA-7)
A ball bearing is released from rest at a height h on
a smooth track and completes the circular loop of
the track. If R is the reaction acting on the ball
bearing at the highest point A of the loop, which of
A small object P of mass 0.3 kg is attached to one
end of a light, rigid rod of length 0.5 m, which is
free to rotate about the other end O as shown. The
object is swung to rotate in a vertical circle so that it
1
attains a speed of 2ms at its topmost position.
What is the force exerted on one end of the rod at
this instant?
11.
A.
a compressive force of 0.6 N
B.
a tensional force of 0.6 N
C.
a tensional force of 2.4 N
D.
a tensional force of 5.4 N
E.
a compressive force of 5.4 N
(97-IIA-4)
The figure shows a car moving round a corner with
a radius of 8 m on a banked road of inclination
20 0 . At what speed would there be no friction
acting on the car along OA?
the following graphs correctly shows the variation
of R with h?
AL-MC-Circular motion / p.4
13.
(99-IIA-8)
A.
N cos  mg
B.
N  mg cos
C.
v2 
gr
sin 
D.
v2 
gr
tan 
E.
N
mv 2

sin 
r
A small ball-bearing is projected with velocity v
from the lowest position P of a vertical circular
15.
(00-IIA-11)
track which is not smooth. The ball-bearing starts
to leave the track at Q. Which of the following
diagrams best represents all the forces acting on
the ball-bearing at Q ?
A student performing a centripetal force
experiment whirls a rubber bung attached to one
end of a string which passes through a glass tube
with smooth openings, and has a weight W hanging
at its other end. The weight of the rubber bung is
much smaller than W. The rubber bung is set into a
horizontal uniform circular motion with angular
speed  while the length of the string beyond the
upper opening of the glass tube is L and this
portion of the string makes an angle  with the
vertical as shown. Which of the following
statements is/are correct?
14.
(00-IIA-8)
(1)
If L is kept constant,  will decrease
with  .
(2)
If  is kept constant, L will increase
with  .
(3)
When W increase,  will increase.
A car of mass m is moving with speed v on a
A.
(1) only
banked road along a circular path of horizontal
B.
(2) only
radius r. The angle of inclination of the road is  . If
C.
(3) only
the centripetal force arises entirely from a
D.
(1) and (2) only
component of the normal reaction N from the road,
E.
(2) and (3) only
which of the following relations is correct?
AL-MC-Circular motion / p.5
16. (01-IIA-10)
A small sphere is connected to one end of a string
which passes through a hole on a horizontal
frictionless board. The other end of the string is
pulled by a downward force F so that the sphere
describes a uniform circular motion with radius r
as shown.
The force F is gradually increased until the radius
reduces steadily to r/2. What is the ratio of the new
kinetic energy of the sphere to its original kinetic
energy? (Neglect any friction between the string
and the hole.)
17.
A.
4:1
B.
2:1
C.
1:1
D.
1:2
E.
1:4
(02-IIA-8)
A particle is moving in a horizontal circle in a
clockwise direction as shown (top view). The
following diagrams show the direction of the
acceleration a of the particle. Which of them is/are
possible?
A.
(1) only
B.
(3) only
C.
(1) and (2) only
D.
(2) and (3) only