Circular Motion
Ranker
PHYSICS TEST
CIRCULAR MOTION
1.
A wheel of perimeter 220 cm rolls on a level road at a speed of 9 km/h. How many
revolutions does the wheel make per second?
A)
3 rev
7 s
B)
3 rev
11 s
C)
25 rev
22 s
D) None of these
2.
A solid cylinder is released from rest from the top of an incline of inclination  and
length l . If the cylinder rolls without slipping, what will be its speed when it reaches the
bottom?
4
2
5
gl sin 
gl sin 
gl sin 
A) gl sin 
B)
C)
D)
3
3
2
3.
A force F acts tangentially at the highest point of a solid sphere of mass m kept on a
rough horizontal plane. If the sphere rolls without slipping, find the acceleration of the
centre of the sphere.
A)
4.
10  F 
 
7 m
B) F/3
C)
3F
2m
D)
5F
7m
A sphere of mass M and radius r shown in figure slips on a rough horizontal plane. At
some instant it has translational velocity v0 and rotational velocity about the centre
v0
.
2r
Find the translational velocity after the sphere starts pure rolling.
w=
v0
2r
r
v0
A
f
A)
5.
3v0
5
B)
2v0
5
C) v0
D)
6
v0
7
A solid sphere, a hollow sphere and a disc, all having same mass and radius , are
placed at the top of a smooth incline and released . Least time will be taken in reaching
the bottom by
A) the solid sphere
B) the hollow sphere
C) the disc
D) all will take same time
Page 1
Circular Motion
6.
Ranker
Solid sphere, a hollow sphere and a disc, all having same mass and radius, are placed at
the top of an incline and released. The friction coefficients between the objects and the
incline are same and not sufficient to allow pure rolling. Least time will be taken in
reaching the bottom by,
7.
A) the solid sphere
B) the hollow sphere
C) the disc
D) all will take same time
In the previous question the smallest kinetic energy at the bottom of the incline will be
achieved by
8.
9.
A) the solid sphere
B) the hollow sphere
C) the disc
D) all will achieve same kinetic energy.
A cylinder rolls on a horizontal plane surface. If the speed of the centre is 25 m/s, what
is the speed of the highest point?
A) 50m/s
B) 100m/s
C) 150m/s
D) 200m/s
A sphere of mass m rolls on a plane surface. Find its kinetic energy at an instant when
its centre moves with speed v .
A)
10.
7 2
mv
5
7 2
mv
2
C)
7
mv 2
10
D)
7 2
mv
6
A string is wrapped over the edge of a uniform disc and the free end is fixed with the
ceiling. The disc moves down, unwinding the string. Find the down ward acceleration
of the disc.
A) g/2
11.
B)
B)
2g
3
C) g/3
D) g/4
A small spherical ball is released from a point at a height h on a rough track shown in
figure. Assuming that it does not slip anywhere find its linear speed when it rolls on the
horizontal part of the track?
h
10g h
3
gh
B) gh
C)
D) None of these
7
5
A small disc is set rolling with a speed v on the horizontal part of the track of the
previous problem from right to left. To what height will it climb up the curved part?
v2
3v 2
v2
3v 2
A)
B)
C)
D)
2g
2g
g
4g
A sphere starts rolling down an incline of inclination  . Find the speed of its centre
when it has covered a distance l .
10g
2
l sin 
gl cos 
A) gl sin 
B) gl cos
C)
D)
7
7
A)
12.
13.
Page 2
Circular Motion
14.
Ranker
Figure shows a rough track, a portion of which is in the form of a cylinder of radius R.
with what minimum linear speed should a sphere of radius r set rolling on the
horizontal part so that it completely goes round the circle on the cylindrical part.
R
15.
16.
17.
18.
19.
20.
21.
27 g  R  r 
7
10
g R  r
7
A thin spherical shell of radius R lying on a rough horizontal surface is hit sharply and
horizontally by a cue. Where should it be hit so that the shell does not slip on the
surface?
R
2R
A) Below the centre
B)
above the centre
2
3
2R
C)
Below the centre
D) None
3
A thin spherically shell lying on a rough horizontal surface is hit by a cue in such a way
that the line of action passes through the centre of the shell. As a result, the shell starts
moving with a linear speed v without any initial angular velocity. Find the linear speed
after it starts pure rolling on the surface.
3v
3v
A)
B) v / 2
C) v / 5
D)
5
4
A hollow sphere of radius R lies on smooth horizontal surface. It is pulled by horizontal
force acting tangentially from the highest point. Find the distance traveled by the sphere
during the time it makes one full rotation.
R
4 R
A) 2 R
B)
C)
D)  R
2
3
A solid sphere of mass 0.50kg is kept on a horizontal surface. The coefficient of static
friction between the surfaces in contact is 2/7. What maximum force can be applied at
the highest point in the horizontal direction so that the sphere does not slip on the
surface? (Take g  10m / s 2 )
A) 1.1N
B) 2.2N
C) 3.3N
D) 4.4N
A small block slides down from the top of a hemisphere of radius r. It is assumed that
there is no friction between the block and hemisphere. At what height h, will the block
loose contact
with the surface of the sphere.
r
2r
r
r
A)
B)
C)
D)
3
3
2
4
Two particles P and Q are located at distance rP and rQ respectively from the centre of
rotating disc such that rP > rQ
A) Both P and Q have the same acceleration
B) Both P and Q do not have the same acceleration
C) P has greater acceleration than Q
D) Q has greater acceleration than P
A)
B)
g  R r
C)
g  R  r
D)
A bucket filled with water is revolved in a vertical circle of radius 4m. If g 10 ms -2, the
time period of revolution will be nearest to
A) 4 s
B) 5 s
C) 8 s
D) 10 s
Page 3
Circular Motion
22.
23.
24.
25.
26.
Ranker
A body of mass ‘m’ is moving in a circle of radius ‘r’ with a constant speed ‘v’. The
work
done by the centripetal force in moving the body over half the circumference of the
circle is
A) mv2 r
B) zero
C) mv2/r
D) r2/mv2
A particle of mass m is describing a circular path of radius r with uniform speed. If L is
the angular momentum of the particle about the axis of the circle, the kinetic energy of
the particle is given by:
A) L2/mr2
B) L2/2mr2
C) 2L2/mr2
D) mr2L
Two particles of equal masses are revolving in circular paths of radii r1 and r2
respectively with the same period. The ratio of their centripetal force is:
r2 / r1
A) r1/r2
B)
C) (r1/r2)2
D) (r2/r1)2
A vehicle is moving with a velocity v on a curved road of width b and radius of
curvature R. For counteracting the centrifugal force on the vehicle, the difference in
elevation required in between the outer and inner edges of the road is:
v 2b
vb 2
vb
vb
A)
B)
C)
D) 2
Rg
Rg
Rg
Rg
A simple pendulum of length L and mass (bob) M is oscillating in a plane about a
vertical line between angular limits   and   . For an angular displacement  where
|  |  |  | the tension T in the string and the velocity V of the bob are related as under in
the above conditions:
MV 2
B) T  Mg cos 
L
A) T cos  =Mg
27.
28.
C) T =Mg cos 
D) none of these
An electric fan has blades of length 30 cm as measured from the axis of rotation. If the
fan is rotating at 1200 rpm, the acceleration of point on the tip of the blade is about:
A) 16000 ms-2
B) 4740 ms-2
C) 2370 ms-2
D) 5055 ms-2
A motor car of mass m travels with a uniform speed v on a convex bridge of radius r.
When the car is at the middle point of the bridge, then the force exerted by the car on
the bridge is
A) mg
29.
30.
B) mg 
mv2
r
C) mg 
mv2
r
D) mg 
mv2
r
A simple pendulum consists of light string from which a spherical bob of mass M is
suspended. The distance between the point of suspension and centre of the bob is l. The
bob
is given a tangential velocity v at the equilibrium position (i.e at the
lowest point). What can be maximum value of velocity v, so that the pendulum
oscillates without the string becoming slack?
A) gl
B) 2gl
C) 4gl
D) 5gl
A weightless thread can support tension up to 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=10ms-2, then the
maximum angular velocity of the stone will be:
A) 5 rad/s
B) 30 rad/s
C) 60 rad/s
D) 10 rad/s
Page 4
Circular Motion
Ranker
KEY
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
C
B
A
D
D
D
B
A
C
B
A
D
C
A
B
A
C
C
B
C
A
B
B
A
A
B
B
C
B
A
Page 5
Circular Motion
Ranker
SOLUTIONS
1.
C
2.
B
v  r
KE =
and
3.
1 2 1 2 3 2
mv  I   mv
2
2
4
3 2
mv  mgl sin 
4
A
F  f  ma (Pseudo) for translational and
2
  2
Fr  fr  I  mr 2    ma
5
r 5
10 F
Solving a 
7 m
4.
D
Initial angular momentum L  Lcm  Mrvo

6
Mrvo
5
Also , the angular momentum about A
 Lcm  Mrv
7
2
v
  Mr 2   Mrv  Mrv
5
5
r
6
7
 Mrvo  Mrv
5
5
6
 v  vo
7
5.
6.
7.
D
Since the surface is smooth, only sliding takes place. Hence all reaches simultaneously
D
In sufficient friction cannot constitute rolling
Hence all reaches simultaneously
B
We have
8.
2
1
2
Mr 2  Mr 2  Mr 2  I solid  I disc  I Hollow
5
2
3
 Hollow sphere haves maximum moment of inertia , for same
A

VH  2Vc  2  25  50m / s
9.
C
1
1
7
KE  mv 2  I  2  mv 2
2
2
10
10.
B
1
  mar
  I   mr 2  
.......1
2
2
r
2g
  ma  mg  a 
3
Page 6
Circular Motion
Ranker
ma
.
mg
11.
A
1 2 1 2
2
mv  I  where I  mr 2
2
2
5
10
v 
gh
7
mgh 
12.
D
1
2
1
2
using mgh  mv 2  I  2
13.
3v2
h
4g
C
k2 2

r2 5
g sin  5 g sin 
a

k2
7
1 2
R
10 gr sin 
Now v 
7
for sphere
h
v
14.
A
mv 2
 mg  v 2   R  r  g............1
Rr
12
1
1
1

Also  mr 2   2  mu 2  mg  2 R  2r   mv2  I  2
25
2
2
2

7
 mg  2 R  r   mg  R  r 
10
 27 R  27r 
71
   mu 2  mg
5 2
10
u
15.
27 g  R  r 
7
B
from law of conservation of angular momentum
mvh  I   mvh 
h
2
 mR2  
3
2
R
3
Page 7
Circular Motion
Ranker
F
.h
R
16.
A
2 2
R  from conservation of angular momentum
3
2
2
5
 vR  VR  R R  VR  VR  vR
3
3
3
5
3
 vR  VR  V  v
3
5
mvR  mVR 
17.
C
2
3F
1
MR 2    
and   ot   t 2 given
3
2 MR
2
1  3F  2
F
2 8MR
2  
and ac 
t  t
2  2 MR 
3F
M
1
4 R
 S  ac t 2 gives S 
2
3
F  R  M  I 
18.
C
f   mg
.
2
F  R  f  R  I   R   mg   MR 2 ......1
5
2
 F   mg  ma
5
 mg  F
a
.........2
M
15 & 2  F = 3.3 N
19.
B
velocity at point s is v  [2 g (r  h)]
centripetal acceleration =
1
2
v2
 g cos
r
2 g (r  h)
h
2r
 g h
r
r
3
20.
C
aR  ( 2 )2  (r )2  r  4   2
21.
same for both P & Q ap > aQ (as rp > rQ)
A
  gR  2 10 T 
22.
 &
2 R
 4s
v
B
Page 8
Circular Motion
23.
Ranker
In circular motion, centripetal force acting on the body is always  r to the velocity
vector.
B
L= mvr   
24.
L
1
, K  mv 2  L2 / 2mr 2
mr
2
A
T1  T2 
2 r1 2 r2
V r

or 1  1
v1
v1
V2 r2
F1 mv12 r2



F2
r1 mv22
2
F  V  r r2 r r
 1   1   2  12  2  1
F2  V2  r1 r2 r1 r2
25.
A
v2
Rg
x
Sin 
b
tan  
x
b
2
x v
v 2b
 
or x 
b Rg
Rg
 sin   tan  
26.
B
Mv 2
T-Mg cos  =
L
27.
B
28.
centripetal acceleration = w2 R =
C
 2 f 
2
R  4740 m / s 2
mv 2
Mg –f =
r
F=mg29.
mv 2
r
B
1
Mgl  Mv 2  V  2 gl
2
30.
A
Page 9
Circular Motion
Ranker



T max  m r 2  g  30  0.5 2  w 2  10

w  5 rad / sec.
Page 10